{"id":35937,"date":"2022-04-04T15:10:00","date_gmt":"2022-04-04T09:40:00","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35937"},"modified":"2022-04-07T11:38:01","modified_gmt":"2022-04-07T06:08:01","slug":"big-ideas-math-algebra-1-answers-chapter-3","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-3\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions"},"content":{"rendered":"<p>Kids who are passionate about solving math calculations and enhance their math skills can refer to this guide. Here we have shared the <strong>Topic wise Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions <\/strong>free pdf. In this BIM Textbook Solution Key of Algebra 1 Ch 3 Graphing Linear functions, you can find various prep resources like Questions from Lessons 3.1 to 3.7 Exercises, practice test questions, chapter tests, cumulative assessments, etc. By using Big Ideas Math Algebra 1 Chapter 3 Answer Key, you can answer all types of questions related to Graphing Linear Functions topics.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 3 Graphing Linear Functions<\/h2>\n<p>Available below links help you to browse step-by-step solutions for all the questions covered in Chapter 3 Graphing Linear Functions<strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\"> Big Ideas Math Algebra 1 Answer Book<\/a><\/strong>. Here, you can see more benefits after referring to the ultimate guide of BIM Algebra 1 Ch 3 Solution Key. Also, students can improve their subject knowledge and problem-solving skills by learning the concepts explained in BIM Math Book Algebra 1 Ch 3 Solutions. Simply click on the provided direct links and practice exercise-wise ch 3 graphing linear function questions of common core 2019 curriculum BIM Textbook to score well.<\/p>\n<ul>\n<li><a href=\"#Graphing_Linear_Functions_Maintaining_Mathematical_Proficiency\">Graphing Linear Functions Maintaining Mathematical Proficiency &#8211; Page 101<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Functions_Mathematical_Practices\">Graphing Linear Functions Mathematical Practices &#8211; Page 102<\/a><\/li>\n<li><a href=\"#Lesson_3.1_Functions\">Lesson 3.1 Functions &#8211; Page (103 &#8211; 110)<\/a><\/li>\n<li><a href=\"#Functions_3.1_Exercises\">Functions 3.1 Exercises &#8211; Page(108-110)<\/a><\/li>\n<li><a href=\"#Lesson_3.2_Linear_Functions\">Lesson 3.2 Linear Functions &#8211; Page(111-120)<\/a><\/li>\n<li><a href=\"#Linear_Functions_3.2_Exercises\">Linear Functions 3.2 Exercises &#8211; Page(117-120)<\/a><\/li>\n<li><a href=\"#Lesson_3.3_Function_Notation\">Lesson 3.3 Function Notation &#8211; Page(121-126)<\/a><\/li>\n<li><a href=\"#Function_Notation_3.3_Exercises\">Function Notation 3.3 Exercises &#8211; Page(125-126)<\/a><\/li>\n<li><a href=\"_Staying_Focused_During_Class\">Graphing Linear Functions Study Skills: Staying Focused During Class &#8211; Page 127<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Functions_3.1_-_3.3_Quiz\">Graphing Linear Functions 3.1 &#8211; 3.3 Quiz &#8211; Page 128<\/a><\/li>\n<li><a href=\"#Lesson_3.4_Graphing_Linear_Equations_in_Standard_Form\">Lesson 3.4 Graphing Linear Equations in Standard Form &#8211; Page(129-134)<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Equations_in_Standard_Form_3.4_Exercises\">Graphing Linear Equations in Standard Form 3.4 Exercises &#8211; Page(133-134)<\/a><\/li>\n<li><a href=\"#Lesson_3.5_Graphing_Linear_Equations_in_Slope-Intercept_Form\">Lesson 3.5 Graphing Linear Equations in Slope-Intercept Form &#8211; Page(135-144)<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Equations_in_Slope-Intercept_Form_3.5_Exercises\">Graphing Linear Equations in Slope-Intercept Form 3.5 Exercises &#8211; Page(141-144)<\/a><\/li>\n<li><a href=\"#Lesson_3.6_Transformations_of_Graphs_of_Linear_Functions\">Lesson 3.6 Transformations of Graphs of Linear Functions &#8211; Page(145-154)<\/a><\/li>\n<li><a href=\"#Transformations_of_Graphs_of_Linear_Functions_3.6_Exercises\">Transformations of Graphs of Linear Functions 3.6 Exercises &#8211; Page(151-154)<\/a><\/li>\n<li><a href=\"#Lesson_3.7_Graphing_Absolute_Value_Functions\">Lesson 3.7 Graphing Absolute Value Functions &#8211; Page(155-162)<\/a><\/li>\n<li><a href=\"#Graphing_Absolute_Value_Functions_3.7_Exercises\">Graphing Absolute Value Functions 3.7 Exercises &#8211; Page(160-162)<\/a><\/li>\n<li><a href=\"_The_Cost_of_a_T-Shirt\">Graphing Linear Functions Performance Task: The Cost of a T-Shirt &#8211; Page 163<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Functions_Chapter_Review\">Graphing Linear Functions Chapter Review &#8211; Page(164-168)<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Functions_Chapter_Test\">Graphing Linear Functions Chapter Test &#8211; Page 169<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Functions_Cumulative_Assessment\">Graphing Linear Functions Cumulative Assessment &#8211; Page (170- 171)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Graphing_Linear_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Graphing Linear Functions Maintaining Mathematical Proficiency<\/h3>\n<p><b>Plot the point in a coordinate plane. Describe the location of the point.<\/b><\/p>\n<p>Question 1.<br \/>\nA(3, 2)<br \/>\nAnswer:<br \/>\nThe given point is: A (3,2)<br \/>\nCompare the given point with (x, y)<br \/>\nSo,<br \/>\nx = 3 and y = 2<br \/>\nHence,<br \/>\nThe representation of the point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 2.<br \/>\nB(-5, 1)<br \/>\nAnswer:<br \/>\nThe given point is: B (-5,1)<br \/>\nCompare the given point with (x, y)<br \/>\nSo,<br \/>\nx = -5 and y = 1<br \/>\nHence,<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 3.<br \/>\nC(0, 3)<br \/>\nAnswer:<br \/>\nThe given point is: c (0,3)<br \/>\nCompare the given point with (x,y)<br \/>\nSo,<br \/>\nx = 0 and y = 3<br \/>\nHence,<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 4.<br \/>\nD(-1, -4)<br \/>\nAnswer:<br \/>\nThe given point is: D (-1,-4)<br \/>\nCompare the given point with (x,y)<br \/>\nSo,<br \/>\nx = -1 and y = -4<br \/>\nHence,<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 5.<br \/>\nE(-3, 0)<br \/>\nAnswer:<br \/>\nThe given point is: E (-3,0)<br \/>\nCompare the given point with (x,y)<br \/>\nSo,<br \/>\nx = -3 and y = 0<br \/>\nHence,<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-6.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-6.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-6-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 6.<br \/>\nF(2, -1)<br \/>\nAnswer:<br \/>\nThe given point is: F (2,-1)<br \/>\nCompare the given point with (x,y)<br \/>\nSo,<br \/>\nx = 2 and y = -1<br \/>\nHence,<br \/>\nThe representation of the given point in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p><b>Evaluate the expression for the given value of x.<\/b><\/p>\n<p>Question 7.<br \/>\n3x &#8211; 4; x = 7<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: 17<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n3x &#8211; 4 with x = 7<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n3 (7) &#8211; 4 = 21 &#8211; 4 = 17<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: 17<\/p>\n<p>Question 8.<br \/>\n-5x + 8; x = 3<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: -7<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n-5x + 8 with x = 3<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n-5 (3) + 8 = -15 + 8 = -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: -7<\/p>\n<p>Question 9.<br \/>\n10x + 18; x = 5<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: 68<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n10x + 18 with x = 5<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n10 (5) + 18 = 50 + 18 = 68<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: 68<\/p>\n<p>Question 10.<br \/>\n-9x &#8211; 2; x = -4<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: 34<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n-9x &#8211; 2 with x = -4<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n-9 (-4) &#8211; 2 = 36 &#8211; 2 = 34<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: 34<\/p>\n<p>Question 11.<br \/>\n24 &#8211; 8x; x = -2<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: 40<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n24 &#8211; 8x with x = -2<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n24 &#8211; 8 (-2) = 24 + 16 = 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: 40<\/p>\n<p>Question 12.<br \/>\n15x + 9; x = -1<br \/>\nAnswer:<br \/>\nThe value of the expression for the given value of x is: -6<\/p>\n<p>Explanation:<br \/>\nThe given expression is:<br \/>\n15x + 9 with x = -1<br \/>\nHence,<br \/>\nThe value of the expression is:<br \/>\n15 (-1) + 9 = -15 + 9 = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the expression for the given value of x is: -6<\/p>\n<p>Question 13.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nLet a and b be positive real numbers. Describe how to plot (a, b), (-a, b), (a, -b), and (-a, -b).<br \/>\nAnswer:<br \/>\nIt is given that a and b are positive real numbers<br \/>\nThe given points are (a, b), (-a, b), (a, -b) and (-a, -b)<br \/>\nLet the names of the points be:<br \/>\nA (a, b), B (-a, b), C (a, -b), and D (-a, -b)<br \/>\nWe know that,<br \/>\nThe coordinate plane is divided into 4 parts. These parts are called\u00a0 &#8220;Quadrants&#8221;<br \/>\nSo,<br \/>\nThe representation of a and b in the 4 quadrants are:<br \/>\n1st Quadrant: (a, b)<br \/>\n2nd Quadrant: (-a, b)<br \/>\n3rd Quadrant: (-a, -b)<br \/>\n4th Quadrant: (a, -b)<br \/>\nHence,<br \/>\nThe representation of the given points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-8.jpg\" alt=\"\" width=\"389\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-8.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-8-300x259.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Functions_Mathematical_Practices\"><\/a>Graphing Linear Functions Mathematical Practices<\/h3>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Determine whether the viewing window is square. Explain.<\/b><\/p>\n<p>Question 1.<br \/>\n-8 \u2264 x \u2264 7, -3 \u2264 y \u2264 7<\/p>\n<p>Question 2.<br \/>\n-6 \u2264 x \u2264 6, -9 \u2264 y \u2264 9<\/p>\n<p>Question 3.<br \/>\n-18 \u2264 x \u2264 18, -12 \u2264 y \u2264 12<\/p>\n<p><b>Use a graphing calculator to graph the equation. Use a square viewing window.<\/b><\/p>\n<p>Question 4.<br \/>\ny = x + 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = x + 3<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3.png\" alt=\"\" width=\"543\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-300x282.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 5.<br \/>\ny = -x &#8211; 2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -x &#8211; 2<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-1.png\" alt=\"\" width=\"537\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-1.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-1-300x287.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 6.<br \/>\ny = 2x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 2x &#8211; 1<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2.png\" alt=\"\" width=\"534\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-2-300x289.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 7.<br \/>\ny = -2x + 1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -2x + 1<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3.png\" alt=\"\" width=\"532\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-3-300x292.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 8.<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 4<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4.png\" alt=\"\" width=\"529\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-4-300x292.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 9.<br \/>\ny = \\(\\frac{1}{3}\\)x + 2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{1}{3}\\)x + 2<br \/>\nNow,<br \/>\nWe can find the values of x and y by putting the values 0, 1, 2&#8230;..<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5.png\" alt=\"\" width=\"549\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-5-300x284.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 10.<br \/>\nHow does the appearance of the slope of a line change between a standard viewing window and a square viewing window?<br \/>\nAnswer:<br \/>\nA typical graphing calculator screen has a height to width ratio of 2 to 3. This means that when you use the standard viewing window of -10 to 10 ( on each axis ), the graph will not be in its true perspective.<br \/>\nTo see a graph in its true perspective, you need to use a square viewing window, in which the tick marks on the x-axis are spaced the same as the tick marks on the y-axis.<\/p>\n<h3><a id=\"Lesson_3.1_Functions\"><\/a>Lesson 3.1 Functions<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>A relation pairs inputs with outputs. When a relation is given as ordered pairs, the x-coordinates are inputs and the y-coordinates are outputs. A relation that pairs each input with exactly one output is a function.<\/p>\n<p><b>EXPLORATION 1<br \/>\nDescribing a Function<br \/>\nWork with a partner.<\/b> Functions can be described in many ways.<\/p>\n<ul>\n<li>by an equation<\/li>\n<li>by an input-output table<\/li>\n<li>using words<\/li>\n<li>by a graph<\/li>\n<li>as a set of ordered pairs<\/li>\n<\/ul>\n<p>a. Explain why the graph is shown represents a function.<br \/>\nAnswer:<br \/>\nThe vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph\u00a0more than once, then the\u00a0graph\u00a0does not define a\u00a0function\u00a0because that x value has more than one output. A\u00a0function\u00a0has only one output value for each input value.<\/p>\n<p>b. Describe the function in two other ways.<br \/>\nAnswer:<br \/>\nThe function can be described in 4 ways. They are:<br \/>\na. A function\u00a0can be\u00a0represented\u00a0verbally.<br \/>\nExample:<br \/>\nThe circumference of a square is four times one of its sides.<br \/>\nb. A function can be represented algebraically.<br \/>\nExample:<br \/>\n3 x + 6 .<br \/>\nc. A function\u00a0can be\u00a0represented\u00a0numerically.<br \/>\nd. A function\u00a0can be\u00a0represented\u00a0graphically.<\/p>\n<p><b>EXPLORATION 2<\/b><\/p>\n<p><b style=\"font-style: inherit;\">Identifying Functions<br \/>\n<\/b><b style=\"font-style: inherit;\">Work with a partner.<\/b> Determine whether each relation represents a function. Explain your reasoning.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 1\" width=\"226\" height=\"178\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-1.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 1.1\" width=\"452\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-1.1.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-1.1-300x208.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><br \/>\ne. (-2, 5), (-1, 8), (0, 6), (1, 6), (2, 7)<br \/>\nf. (-2, 0), (-1, 0), (-1, 1), (0, 1), (1, 2), (2, 2)<br \/>\ng. Each radio frequency x in a listening area has exactly one radio station y.<br \/>\nh. The same television station x can be found on more than one channel y.<br \/>\ni. x = 2<br \/>\nj. y = 2x + 3<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nFunctions can be described in different ways. They are:<br \/>\na. By an equation<br \/>\nb. By an input-output table<br \/>\nc. Using words<br \/>\nd. By a graph<br \/>\ne. As a set of ordered pairs<br \/>\nWe know that,<br \/>\nA function has only a single input for each or multiple outputs<br \/>\nHence,<br \/>\nThe given Exercises above i.e., a, e, g,\u00a0 j are the relations that represent a function and the remaining relations are not functions<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nWhat is a function? Give examples of relations, other than those in Explorations 1 and 2, that (a) are functions and (b) are not functions.<br \/>\nAnswer:<br \/>\nDefinition of Function:<br \/>\nA relation from a set of inputs to a set of possible outputs where each input is related to exactly one output is known as &#8221; Function&#8221;<br \/>\nExamples of relation that is a function:<br \/>\na. y = x + 3<br \/>\nb. y = -x\u00b2 + 1<br \/>\nExample of relation that is not a function:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-56837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-6.png\" alt=\"\" width=\"280\" height=\"180\" \/><br \/>\nWe know that,<br \/>\nA relation is a set of inputs for specific outputs.<br \/>\nBut from the above,<br \/>\nA single input has multiple outputs<\/p>\n<p><b>3.1 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Determine whether the relation is a function. Explain.<\/b><\/p>\n<p>Question 1.<br \/>\n(-5, 0), (0, 0), (5, 0), (5, 10)<br \/>\nAnswer:<br \/>\nThe given relation is:<br \/>\n(-5, 0), (0, 0), (5, 0), (5, 10)<br \/>\nFrom the given relation,<br \/>\nWe know that,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input should correspond with only one output<br \/>\nBut,<br \/>\nWhen we observe the given relation, there are 2 outputs for a single input<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is not a function<\/p>\n<p>Question 2.<br \/>\n(-4, 8), (-1, 2), (2, -4), (5, -10)<br \/>\nAnswer:<br \/>\nThe given relation is:<br \/>\n(-4, 8), (-1, 2), (2, -4), (5, -10)<br \/>\nFrom the given relation,<br \/>\nWe know that,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input should correspond with only one output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 2\" width=\"182\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 2\" width=\"182\" height=\"110\" \/><br \/>\nThe representation of the table in the form of relation is:<br \/>\n(2, 2.6), (4, 5.2), (6, 7.8)<br \/>\nFrom the given relation,<br \/>\nWe know that,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input should correspond with only one output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 3\" width=\"144\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 3\" width=\"144\" height=\"122\" \/><br \/>\nThe representation of the given figure in the form of relation is:<br \/>\n(1, -2), (1, 0), (2, 4)<br \/>\nFrom the given relation,<br \/>\nWe know that,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input should correspond with only one output<br \/>\nBut,<br \/>\nWhen we observe the given relation, there are 2 outputs for a single input<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is not a function<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Determine whether the graph represents a function. Explain.<\/b><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 4\" width=\"176\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 4\" width=\"176\" height=\"151\" \/><br \/>\nThe representation of the points from the graph is:<br \/>\n(0, 3), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3)<br \/>\nFrom the given relation,<br \/>\nWe know that,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input should correspond with only one output<br \/>\nWe have to remember that the inputs must be different but outputs may be the same or different<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a function<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 5\" width=\"177\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 5\" width=\"177\" height=\"151\" \/><br \/>\nFrom the graph,<br \/>\nThe representation of the points are:<br \/>\n(2, 1), (1, 2), (1, 3), (1, 4), (0.5, 5), (0.5, 6), (3, 0), (4, 1), (4.2, 2), (4.8, 3), (5, 4), (5.1, 5), (5.1, 6)<br \/>\nFrom the points,<br \/>\nWe can observe that the output is different for the same input<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is not a function<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 6\" width=\"175\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 6\" width=\"175\" height=\"156\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that for the same value of x, there are different values of y<br \/>\nWhere,<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nWe know that,<br \/>\nFor a function, each input must be matched with a single output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is not a function<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 7\" width=\"175\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 7\" width=\"175\" height=\"156\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that there are multiple outputs for a single input<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is not a function<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Find the domain and range of the function represented by the graph.<\/b><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 8\" width=\"136\" height=\"129\" \/><\/p>\n<p>Answer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 8\" width=\"136\" height=\"129\" \/><br \/>\nWe know that,<br \/>\n&#8220;Domain&#8221; is defined as the set of all values present in the x-axis<br \/>\n&#8220;Range&#8221; is defined as the set of all values present in the y-axis<br \/>\nHence,<br \/>\nThe domain of the given graph is: -2, -1, 0, 1, 2<br \/>\nThe range of the given graph is: 1, 2, 3,\u00a0 4<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 9\" width=\"159\" height=\"144\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 9\" width=\"159\" height=\"144\" \/><br \/>\nWe know that,<br \/>\n&#8220;Domain&#8221; is defined as the set of all values present in the x-axis<br \/>\n&#8220;Range&#8221; is defined as the set of all values present in the y-axis<br \/>\nHence,<br \/>\nThe domain of the given graph is: 1, 2, 3, 4, 5<br \/>\nThe range of the given graph is: 0, 1, 2, 3,\u00a0 4<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 11.<br \/>\nThe function a = -4b + 14 represents the number &#8216;a&#8217; of avocados you have left after making b batches of guacamole.<br \/>\na. Identify the independent and dependent variables.<br \/>\nAnswer:<br \/>\nThe &#8220;Independent variable&#8221; represents the input values of a function and can be any value in the domain.<br \/>\nThe dependent variable represents the output values of the function and depends on the value of the independent variable<br \/>\nHence, from the above,<br \/>\nThe independent variable is: b (batches of guacamole)<br \/>\nThe dependent variable is: a ( The number of avocados )<\/p>\n<p>b. The domain is 0, 1, 2, and 3. What is the range?<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\na = -4b + 14<br \/>\nIn the given function,<br \/>\nInput: b<br \/>\nOutput: a<br \/>\nWe know that,<br \/>\nThe &#8220;Domain&#8221; is defined as the set of all values present in the input or the x-axis<br \/>\nThe given Domain is: 0, 1, 2, and 3<br \/>\nSo,<br \/>\nTo find the range, we have to find the values of b for each value present in the domain<br \/>\nSo,<br \/>\na = -4 (0) + 14 = 14<br \/>\na = -4 (1) + 14 = 10<br \/>\na = -4 (2) + 14 = 6<br \/>\na = -4 (3) + 14 = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the range for the given equation is: 2,\u00a0 6, 10, and 14<\/p>\n<p>Question 12.<br \/>\nThe function t = 19m + 65 represents the temperature t (in degrees Fahrenheit) of an oven after preheating for m minutes.<br \/>\na. Identify the independent and dependent variables.<br \/>\nAnswer:<br \/>\nThe &#8220;Independent variable&#8221; represents the input values of a function and can be any value in the domain.<br \/>\nThe dependent variable represents the output values of the function and depends on the value of the independent variable<br \/>\nHence, from the above,<br \/>\nThe independent variable is: Minutes<br \/>\nThe dependent variable is: Temperature<\/p>\n<p>b. A recipe calls for an oven temperature of 350\u00b0F. Describe the domain and range of the function.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nt = 19m + 65<br \/>\nCompare the given function with<br \/>\ny = mx + c<br \/>\nIt is given that a recipe calls for an oven temperature of 350\u00b0F<br \/>\nSo,<br \/>\n350 = 19m + 65<br \/>\n19m = 350 &#8211; 65<br \/>\n19m = 285<br \/>\nm = 285 \/ 19<br \/>\nm = 15 minutes<br \/>\nSo,<br \/>\nt = 19 (15) + 350<br \/>\nt = 285 + 65<br \/>\nt = 350\u00b0F<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given function is: 0 \u2264 m \u2264 15 [ Since the minutes will not be -ve ]<br \/>\nThe range of the given function is: 65 \u2264 t \u2264 350 [ Since the\u00a0 minimum temperature is the value of c ]<\/p>\n<h3><a id=\"Functions_3.1_Exercises\"><\/a>Functions 3.1 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nHow are independent variables and dependent variables different?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 1\" width=\"587\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-1.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-1-300x58.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>DIFFERENT WORDS, SAME QUESTION<\/b><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-9.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 9.1\" width=\"597\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-9.1.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-9.1-300x63.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><br \/>\nAnswer:<br \/>\nThe given statements are:<br \/>\na. Find the range of the function represented by the table?<br \/>\nb. Find the inputs of the function represented by the table?<br \/>\nc. Find the x values of the function represented by (-1, 7), (0, 5), and (1, -1)?<br \/>\nd. Find the domain of the function represented by (-1, 7), (0, 5), and (1, -1)?<br \/>\nNow,<br \/>\nFrom the given table,<br \/>\nThe values of x are: -1, 0, 1<br \/>\nThe values of y are: 7, 5, -1<br \/>\nWe know that,<br \/>\nFor a function,<br \/>\nThe x values represent the input and the domain<br \/>\nThe y values represent the output and the range<br \/>\nSo,<br \/>\na.<br \/>\nThe range of the function represented by the table is: 7, 5, -1<br \/>\nb.<br \/>\nThe inputs of the function represented by the table are: -1, 0, 1<br \/>\nc.<br \/>\nThe x values of the function represented by the given points are: -1, 0, 1<br \/>\nd.<br \/>\nThe domain of the function represented by the given points are: -1, 0, 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that all the given four are the same<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20138, determine whether the relation is a function. Explain.<\/b><\/p>\n<p>Question 3.<br \/>\n(1, -2), (2, 1), (3, 6), (4, 13), (5, 22)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 3\" width=\"366\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-3.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-3-300x27.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Question 4.<br \/>\n(7, 4), (5, -1), (3, -8), (1, -5), (3, 6)<br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\n(7, 4), (5, -1), (3, -8), (1, -5), (3, 6)<br \/>\nWe know that,<br \/>\nFor a function, each input has only a single output<br \/>\nBut from the above,<br \/>\nWe can observe that 3 has multiple outputs<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is not a function<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 10\" width=\"145\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 5\" width=\"381\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-5.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-5-300x28.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 11\" width=\"143\" height=\"145\" \/><br \/>\nAnswer:<br \/>\nThe given relation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 11\" width=\"143\" height=\"145\" \/><br \/>\nWe know that,<br \/>\nFor a function, a single input has a single output<br \/>\nHence, from the above,<br \/>\nWe can say that each input has only 1 output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 12\" width=\"289\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 7\" width=\"549\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-7.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-7-300x33.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 13\" width=\"285\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 13\" width=\"285\" height=\"69\" \/><br \/>\nFrom the given table,<br \/>\nWe can observe that each input has a single output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p><b>In Exercises 9\u201312, determine whether the graph represents a function. Explain.<\/b><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-14.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 14\" width=\"142\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 9\" width=\"536\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-9.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-9-300x35.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 15\" width=\"150\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 15\" width=\"150\" height=\"150\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that the vertical line can be drawn through more than one point on the graph i.e., input 2 has repeated 2 times i.e., (2, 1) and (2, 5)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is not a function<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-16.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 16\" width=\"142\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 11\" width=\"565\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-11.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-11-300x31.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 17\" width=\"164\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 17\" width=\"164\" height=\"132\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that each input corresponds to a single output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a function<\/p>\n<p><b>In Exercises 13\u201316, find the domain and range of the function represented by the graph.<\/b><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-18.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 18\" width=\"131\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 13\" width=\"520\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-13.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-13-300x80.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 19\" width=\"135\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 19\" width=\"135\" height=\"135\" \/><br \/>\nFrom the given graph,<br \/>\nThe ordered pairs are: (0, 4), (-2, 4), (2, 4), (4, 4)<br \/>\nHence,<br \/>\nThe domain of the given graph is: 0, -2, 2, 4<br \/>\nThe range of the given graph is: 4<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-20.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 20\" width=\"136\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 15\" width=\"500\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-15.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-15-300x58.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 21\" width=\"149\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 21\" width=\"149\" height=\"146\" \/><br \/>\nFrom the given graph,<br \/>\nIdentify the x and y values<br \/>\nSo,<br \/>\nThe values of x range from 2 to 7 excluding 2 and 7<br \/>\nThe values of y range from 1 to 6 excluding 1 and 6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given graph is: 2 &lt; x &lt; 7<br \/>\nThe range of the given graph is: 1 &lt; y &lt; 6<\/p>\n<p>Question 17.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function y = 25x + 500 represents your monthly rent y (in dollars) when you pay x days late.<br \/>\na. Identify the independent and dependent variables.<br \/>\nb. The domain is 0, 1, 2, 3, 4, and 5. What is the range?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 17\" width=\"555\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-17.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-17-300x231.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 18.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function y = 3.5x + 2.8 represents the cost y (in dollars) of a taxi ride of x miles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-22.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 22\" width=\"294\" height=\"173\" \/><br \/>\na. Identify the independent and dependent variables.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 3.5x + 2.8<br \/>\nFrom the above function,<br \/>\nThe independent variable is: x which represents the number of miles<br \/>\nThe dependent variable is: y which represents the cost in dollars<\/p>\n<p>b. You have enough money to travel at most 20 miles in a taxi. Find the domain and range of the function.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 3.5x + 2.8<br \/>\nIt is given that you have enough money to travel at most 20 miles i.e., the value of x in a taxi i.e.,<br \/>\nx \u2265 0 and x \u2264 20<br \/>\nSo,<br \/>\nThe value of x ranges from 0 \u2264 x \u2264 20<br \/>\nNow,<br \/>\ny = 3.5 (20) + 2.8<br \/>\ny = 7 + 2.8<br \/>\ny = $9.8<br \/>\ny = 3.5 (0) + 2.8<br \/>\ny = 0 + 2.8<br \/>\ny = $2.8<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given function is: 0 \u2264 x \u2264 20 miles<br \/>\nThe range of the given function is: $2.8 \u2264 y \u2264 $9.8<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 19 and 20, describe and correct the error in the statement about the relation shown in the table.<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-23.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 23\" width=\"309\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-23.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-23-300x74.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-24.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 24\" width=\"334\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-24.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-24-300x68.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 19\" width=\"591\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-19.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-19-300x60.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-25.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 25\" width=\"337\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-25.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-25-300x66.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nAnswer:<br \/>\nIt is given that the relation is a function and the range is 1, 2, 3, 4, and 5<br \/>\nWe know that,<br \/>\nThe relation is a function only when a single input pairs with an output<br \/>\nFor the function, the domain, and the range exist<br \/>\nFrom the given table,<br \/>\nThe domain is: 1, 2, 3, 4, 5<br \/>\nThe range is: 6, 7, 8, 6, 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is not correct<\/p>\n<p><b>ANALYZING RELATIONSHIPS<br \/>\nIn Exercises 21 and 22, identify the independent and dependent variables.<\/b><\/p>\n<p>Question 21.<br \/>\nThe number of quarters you put into a parking meter affects the amount of time you have on the meter.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 21\" width=\"576\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-21.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-21-300x58.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 22.<br \/>\nThe battery power remaining on your MP3 player is based on the amount of time you listen to it.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nThe battery power remaining on your MP3 player is based on the amount of time you listen to it.<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe Independent variable: Amount of time<br \/>\nThe dependent variable: Battery power<\/p>\n<p>Question 23.<br \/>\n<b>MULTIPLE REPRESENTATIONS<\/b><br \/>\nThe balance y (in dollars) of your savings account is a function of the month x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-26.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 26\" width=\"298\" height=\"83\" \/><br \/>\na. Describe this situation in words.<br \/>\nb. Write the function as a set of ordered pairs.<br \/>\nc. Plot the ordered pairs in a coordinate plane.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 23\" width=\"574\" height=\"416\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-23.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-23-300x217.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>MULTIPLE REPRESENTATIONS<\/b><br \/>\nThe function 1.5x + 0.5y = 12 represents the number of hardcover books x and softcover books y you can buy at a used book sale.<br \/>\na. Solve the equation for y.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\n1.5x + 0.5y = 12<br \/>\nSo,<br \/>\n0.5y = 12 &#8211; 1.5x<br \/>\ny = \\(\\frac{12 &#8211; 1.5x}{0.5}\\)<br \/>\ny = \\(\\frac{12}{0.5}\\) &#8211; \\(\\frac{1.5x}{0.5}\\)<br \/>\ny = 24 &#8211; 3x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation for y is:<br \/>\ny = 24 &#8211; 3x<\/p>\n<p>b. Make an input-output table to find ordered pairs for the function.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe equation for y is:<br \/>\ny = 24 &#8211; 3x<br \/>\nNow,<br \/>\nPut the values of 0, 1, 2, 3 in x<br \/>\nSo,<br \/>\ny = 24 &#8211; 3(0) = 24<br \/>\ny = 24 &#8211; 3(1) = 21<br \/>\ny = 24 &#8211; 3(2) = 18<br \/>\ny = 24 &#8211; 3 (3) = 15<br \/>\nHence,<br \/>\nThe input-output table for the given equation of y is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-12.jpg\" alt=\"\" width=\"201\" height=\"63\" \/><\/p>\n<p>c. Plot the ordered pairs in a coordinate plane.<br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nThe table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-12.jpg\" alt=\"\" width=\"201\" height=\"63\" \/><br \/>\nWe know that,<br \/>\nThe ordered pair is in the form of (x, y)<br \/>\nFrom the table,<br \/>\nThe ordered pairs are:<br \/>\n(0, 24), (1, 21), (2, 18), (3, 15)<br \/>\nHence,<br \/>\nThe representation of the ordered pairs in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7.png\" alt=\"\" width=\"499\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-7-150x150.png 150w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 25.<br \/>\n<b>ATTENDING TO PRECISION<\/b><br \/>\nThe graph represents a function. Find the input value corresponding to an output of 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-27.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 27\" width=\"146\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 25\" width=\"87\" height=\"34\" \/><\/p>\n<p>Question 26.<br \/>\n<b>OPEN-ENDED<\/b><br \/>\nFill in the table so that when t is the independent variable, the relation is a function, and when t is the dependent variable, the relation is not a function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-28.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 28\" width=\"211\" height=\"72\" \/><br \/>\nAnswer:<br \/>\nLet the function in terms of t and v\u00a0 such as t is the independent variable and v is the dependent variable is:<br \/>\nv = t + 4 &#8212;&#8212;&#8212;&#8211;(1)<br \/>\nLet the function in terms of t and v\u00a0 such as v is the independent variable and t is the dependent variable is:<br \/>\nt = 4v &#8212;&#8212;&#8212;&#8211;(2)<br \/>\nNow,<br \/>\nplace the values 0, 1, 2, 3 &#8230;&#8230;.. in the independent variables of both functions<br \/>\nNow,<br \/>\nIn equation (1),<br \/>\nv = 0 + 4 = 4<br \/>\nv = 1 + 4 = 5<br \/>\nv = 2 + 4 = 6<br \/>\nv = 3 + 4 = 7<br \/>\nIn equation (2),<br \/>\nt = 4(0) = 0<br \/>\nt = 4(1) = 4<br \/>\nt = 4(2) = 8<br \/>\nt = 4(3) = 12<br \/>\nHence,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-11.jpg\" alt=\"\" width=\"201\" height=\"97\" \/>\u00a0 \u00a0 \u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-57524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10.jpg\" alt=\"\" width=\"201\" height=\"85\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that equation (1) is a function and equation (2) is not a function<\/p>\n<p>Question 27.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nYou select items in a vending machine by pressing one letter and then one number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-29.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 29\" width=\"357\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-29.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-29-300x246.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\na. Explain why the relation that pairs letter-number combinations with food or drink items is a function.<br \/>\nb. Identify the independent and dependent variables.<br \/>\nc. Find the domain and range of the function<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 27\" width=\"570\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-27.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-27-300x154.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe graph represents the height h of a projectile after t seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-30.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 30\" width=\"242\" height=\"174\" \/><br \/>\na. Explain why h is a function of t.<br \/>\nb. Approximate the height of the projectile after 0.5 seconds and after 1.25 seconds.<br \/>\nc. Approximate the domain of the function.<br \/>\nd. Is t a function of h? Explain.<br \/>\nAnswer:<br \/>\na.<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-30.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 30\" width=\"242\" height=\"174\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that when we draw the vertical lines, each vertical line corresponds to only 1 value.<br \/>\nHence, from the above,<br \/>\nWe can conclude that h is a function of t by using the vertical line method<\/p>\n<p>b.<br \/>\nFrom the given graph,<br \/>\nWe can observe that the height of the projectile after 0.5 seconds increases and after some time, the height of the projectile decreases<br \/>\nWe can observe that the height of the projectile after 1.25 seconds decreases steadily<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe approximate maximum height after 0.5 seconds is: 30 feet<br \/>\nThe approximate maximum height after 1.25 seconds is: 25 feet<\/p>\n<p>c.<br \/>\nFrom the given graph,<br \/>\nThe values of t in the x-axis vary from 0 to 2.5<br \/>\nHence,<br \/>\nThe domain of the given graph is: 0 \u2264 t \u2264 2.5 seconds<\/p>\n<p>d.<br \/>\nt is not a function of h<br \/>\nReason:<br \/>\nWhen we observe the graph,<br \/>\nWe can see that for a single value of t, there are multiple values of h.<br \/>\nWe know that a relation can be considered as a function only when a single input pairs with a single output<br \/>\nhence, from the above,<br \/>\nWe can conclude that that t is not a function of h<\/p>\n<p>Question 29.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend says that a line always represents a function. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 29\" width=\"438\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-29.png 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-29-300x25.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p>Question 30.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nWrite a function in which the inputs and\/or the outputs are not numbers. Identify the independent and dependent variables. Then find the domain and range of the function.<br \/>\nAnswer:<br \/>\nIt is given that the inputs and\/or the outputs will not be numbers.<br \/>\nSo,<br \/>\nThe given function in which the inputs and\/or the outputs are not numbers is:<br \/>\n\u00b0C = 32 + \u00b0F<br \/>\nFrom the given function,<br \/>\nThe independent variable is: \u00b0F<br \/>\nThe dependent variable is: \u00b0C<br \/>\nNow,<br \/>\nFrom the given function,<br \/>\nWe can observe that the values of \u00b0F vary from -\u221e to \u221e<br \/>\nNow,<br \/>\nPlace the values of -\u221e to \u221e in the place of \u00b0F<br \/>\nSo,<br \/>\n\u00b0C = 32 + 0 = 32\u00b0F<br \/>\n\u00b0C = 32 + 1 = 33\u00b0F<br \/>\n\u00b0C = 32 &#8211; 1 = 31\u00b0F<br \/>\n\u00b0C = 32 &#8211; 40 = -8\u00b0F<br \/>\nHence, from the above values,<br \/>\nWe can observe that the values of \u00b0C vary from -\u221e to \u221e<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the function is: -\u221e to \u221e<br \/>\nThe range of the function is: -\u221e to \u221e<\/p>\n<p><b>ATTENDING TO PRECISION In Exercises 31\u201334, determine whether the statement uses the word function in a way that is mathematically correct. Explain your reasoning.<\/b><\/p>\n<p>Question 31.<br \/>\nThe selling price of an item is a function of the cost of making the item.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 31\" width=\"583\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-31.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-31-300x32.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 32.<br \/>\nThe sales tax on a purchased item in a given state is a function of the selling price.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nThe sales tax on a purchased item in a given state is a function of the selling price<br \/>\nWe know that,<br \/>\nThe sales tax is a percentage applied to the selling price<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement uses the word function in a way that is mathematically correct.<\/p>\n<p>Question 33.<br \/>\nA function pairs each student in your school with a homeroom teacher.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 33\" width=\"582\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-33.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-33-300x29.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 34.<br \/>\nA function pairs each chaperone on a school trip with 10 students.<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nA function pairs each chaperone on a school trip with 10 students.<br \/>\nWe know that,<br \/>\nEach chaperone on a school trip pairs with more than 1 student i.e., the number may be 2 or \u221e but not exactly 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement does not use the word function in a way that is mathematically correct.<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 35\u201338, tell whether the statement is true or false. If it is false, explain why.<\/b><\/p>\n<p>Question 35.<br \/>\nEvery function is a relation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 35\" width=\"53\" height=\"25\" \/><\/p>\n<p>Question 36.<br \/>\nEvery relation is a function.<br \/>\nAnswer:<br \/>\nThe given statement is false<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nEvery function is a relation that has only 1 output for a single input<br \/>\nBut we can not say that every relation has a single output for a single input<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is false<\/p>\n<p>Question 37.<br \/>\nWhen you switch the inputs and outputs of any function, the resulting relation is a function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 37\" width=\"584\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-37.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-37-300x71.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 38.<br \/>\nWhen the domain of a function has an infinite number of values, the range always has an infinite number of values.<br \/>\nAnswer:<br \/>\nThe given statement is false<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nThe domain is defined as the set of all the values of x<br \/>\nThe range is defined as the set of all the values of y<br \/>\nNow, consider an example<br \/>\nLet the input be x<br \/>\nLet the output be a constant<br \/>\nNow,<br \/>\nThe domain of the input can vary from -\u221e to \u221e<br \/>\nBut the range of the output is only a constant even though we put any value of x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given statement is false<\/p>\n<p>Question 39.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nConsider the triangle shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-31.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 31\" width=\"120\" height=\"136\" \/><br \/>\na. Write a function that represents the perimeter of the triangle.<br \/>\nb. Identify the independent and dependent variables.<br \/>\nc. Describe the domain and range of the function. (Hint: The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 39\" width=\"598\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-39.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-39-300x148.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p><b>REASONING<br \/>\nIn Exercises 40\u201343, find the domain and range of the function.<\/b><\/p>\n<p>Question 40.<br \/>\ny = | x |<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = | x |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nWe can put the values of x from -\u221e to \u221e<br \/>\nSo,<br \/>\nThe values of x vary from 0 to \u221e since x can&#8217;t be negative<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given function is: -\u221e to \u221e<br \/>\nThe range of the given function is: 0 to \u221e<\/p>\n<p>Question 41.<br \/>\ny = &#8211; | x |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 41\" width=\"578\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-41.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-41-300x59.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 42.<br \/>\ny = | x | &#8211; 6<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = | x | &#8211; 6<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nWe can vary the values of x from -\u221e to \u221e<br \/>\nThe values of y vary from -6 to \u221e<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given function is: -\u221e to \u221e<br \/>\nThe range of the given function is: y \u2265 -6<\/p>\n<p>Question 43.<br \/>\ny = 4 &#8211; | x |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 43\" width=\"578\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-43.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-43-300x58.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Write the sentence as an inequality.<\/b> (Section 2.1)<\/p>\n<p>Question 44.<br \/>\nA number y is less than 16.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nA number y is less than 16<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\ny &lt; 16<\/p>\n<p>Question 45.<br \/>\nThree is no less than a number x.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 45\" width=\"60\" height=\"35\" \/><\/p>\n<p>Question 46.<br \/>\nSeven is at most the quotient of a number d and -5.<br \/>\nAnswer:<br \/>\nThe given worded form is:<br \/>\nSeven is at most the quotient of a number d and -5<br \/>\nHence,<br \/>\nThe representation of the given worded form in the form of inequality is:<br \/>\n7 \u2264 d \u00f7 (-5)<\/p>\n<p>Question 47.<br \/>\nThe sum of a number w and 4 is more than -12.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 47\" width=\"134\" height=\"32\" \/><\/p>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 48.<br \/>\n11<sup>2<br \/>\n<\/sup><span style=\"font-size: 16px;\">Answer:<br \/>\nThe product of 11\u00b2 is:<br \/>\n11\u00b2 = 11 \u00d7 11 = 121<\/span><\/p>\n<p>Question 49.<br \/>\n(-3)<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 49\" width=\"335\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-49.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-49-300x32.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 50.<br \/>\n-5<sup>2<br \/>\n<\/sup><span style=\"font-size: 16px;\">Answer:<br \/>\nThe product of -5\u00b2 is:<br \/>\n-5\u00b2 = -5 \u00d7 -5 = 25 [ We know that &#8211; \u00d7 &#8211; = + ]<\/span><\/p>\n<p>Question 51.<br \/>\n2<sup>5<br \/>\n<\/sup><span style=\"font-size: 16px;\">Answer:<\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.1-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.1 Question 51\" width=\"250\" height=\"28\" \/><\/p>\n<h3><a id=\"Lesson_3.2_Linear_Functions\"><\/a>Lesson 3.2 Linear Functions<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you determine whether a function is linear or non-linear?<br \/>\nAnswer:<br \/>\nSimplify the equation as closely as possible to the form of y = mx + c.<br \/>\nCheck to see if your\u00a0equation has exponents.<br \/>\nIf\u00a0it has exponents, it is\u00a0nonlinear.\u00a0If your\u00a0equation has no exponents, it is\u00a0linear.<\/p>\n<p><b>EXPLORATION 1<br \/>\nFinding Patterns for Similar Figures<\/b><br \/>\n<b>Work with a partner.<\/b> Copy and complete each table for the sequence of similar figures. (In parts (a) and (b), use the rectangle shown.) Graph the data in each table. Decide whether each pattern is linear or nonlinear. Justify your conclusion.<br \/>\na. perimeters of similar rectangles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-32.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 32\" width=\"185\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe perimeter of the rectangle (P) = 2 (Length + Width)<br \/>\nP = 2 (x + 2x)<br \/>\nP = 2 (3x)<br \/>\nP = 6x<br \/>\nHence,<br \/>\nThe completed table for the perimeters of similar rectangles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-13.jpg\" alt=\"\" width=\"236\" height=\"58\" \/><br \/>\nThe representation of the perimeters of the similar rectangles in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10.png\" alt=\"\" width=\"519\" height=\"509\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10-300x294.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>b. areas of similar rectangles<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-32.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 32\" width=\"185\" height=\"118\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nArea of the rectangle (A) = Length \u00d7 Width<br \/>\nA = x \u00d7 (2x)<br \/>\nA = 2x\u00b2<br \/>\nHence,<br \/>\nThe complete table for the area of the similar rectangles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-14.jpg\" alt=\"\" width=\"261\" height=\"58\" \/><br \/>\nThe representation of the areas of the similar rectangles in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-9.png\" alt=\"\" width=\"541\" height=\"519\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-9.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-9-300x288.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\nc. circumferences of circles of radius r<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe circumference of circle = 2\u03c0r<br \/>\nTake the value of \u03c0 as 3<br \/>\nHence,<br \/>\nThe complete table for the circumferences of circles of radius r is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-15.jpg\" alt=\"\" width=\"247\" height=\"68\" \/><br \/>\nThe representation of the circumferences of the circles in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10.png\" alt=\"\" width=\"519\" height=\"509\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-10-300x294.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>d. areas of circles of radius r<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe area of the circle = \u03c0r\u00b2<br \/>\nTake the value of \u03c0 as 3<br \/>\nHence,<br \/>\nThe complete table for the areas of the similar circles is:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-57950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-16.jpg\" alt=\"\" width=\"245\" height=\"61\" \/><br \/>\nThe representation of the areas of the similar circles is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-57973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-11.png\" alt=\"\" width=\"537\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-11.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-11-300x288.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow do you know that the patterns you found in Exploration 1 represent functions?<br \/>\nAnswer:<br \/>\nIn Exploration 1,<br \/>\nFrom the graphs,<br \/>\nWe can observe that from the vertical test, only one point passes through each vertical line i.e., each input hs only 1 output<br \/>\nOur observation coincides with the definition of function<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given patterns in Exploration 1 represent functions<\/p>\n<p>Question 3.<br \/>\nHow can you determine whether a function is linear or nonlinear?<br \/>\nAnswer:<br \/>\nSimplify the equation as closely as possible to the form of y = mx + c.<br \/>\nCheck to see if your\u00a0equation has exponents.<br \/>\nIf\u00a0it has exponents, it is\u00a0nonlinear.\u00a0If your\u00a0equation has no exponents, it is\u00a0linear.<\/p>\n<p>Question 4.<br \/>\nDescribe two real-life patterns: one that is linear and one that is nonlinear. Use patterns that are different from those described in Exploration 1.<br \/>\nAnswer:<br \/>\nThe real-life pattern that is linear is:<br \/>\nThe distance you travel when you go for a jog, you can graph the function and make some assumptions with only two points. The slope of a function is the same as the rate of change for the dependent variable (y), For instance, if you&#8217;re graphing distance Vs<br \/>\nThe real-life pattern that is non-linear is:<br \/>\nTriangulation of GPS signals<br \/>\nExample:<br \/>\nA device like your cellphone receives signals from GPS satellites, which have known orbital positions around the Earth.<\/p>\n<p><b>3.2 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Does the graph or table represent a linear or nonlinear function? Explain.<\/b><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-36.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 36\" width=\"165\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-36.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 36\" width=\"165\" height=\"154\" \/><br \/>\nThe graph represents a straight line<br \/>\nWe know that,<br \/>\nThe straight line will be in the form of<br \/>\ny = mx + c or y = mx<br \/>\nWhere,<br \/>\nm is the slope-intercept<br \/>\nc is the y-intercept that cuts through the y-axis<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is linear function<\/p>\n<p><span style=\"font-size: 16px;\">Question 2.<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-37.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 37\" width=\"163\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-37.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 37\" width=\"163\" height=\"155\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that the graph is not a straight line i.e., it is not linear<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a non-linear function<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-38.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 38\" width=\"202\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-38.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 38\" width=\"202\" height=\"68\" \/><br \/>\nFrom the given table,<br \/>\nWe can observe that<br \/>\nThere is a constant difference of 1 between the values of x and there is a constant difference of 2 between the values of y<br \/>\nThe difference is constant for both the values of x and y<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given table is a linear function<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-39.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 39\" width=\"202\" height=\"74\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-39.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 39\" width=\"202\" height=\"74\" \/><br \/>\nFrom the given table,<br \/>\nWe can observe that<br \/>\nThere is a constant difference of 1 between the values of x and there is a constant ratio of 2 between the values of y.<br \/>\nSince the operations are different between the values of x and y,<br \/>\nWe can conclude that the given table is a non-linear function<\/p>\n<p><b>Does the equation represent a linear or nonlinear function? Explain.<\/b><\/p>\n<p>Question 5.<br \/>\ny = x + 9<br \/>\nAnswer:<br \/>\nThe given equation represents the linear function<\/p>\n<p>Explanation:<br \/>\nThe given function is:<br \/>\ny = x + 9<br \/>\nWe know that,<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nWhen we compare the given equation with the standard representation of linear function,<br \/>\nWe can conclude that the given equation is a linear function<\/p>\n<p>Question 6.<br \/>\ny = \\(\\frac{3 x}{5}\\)<br \/>\nAnswer:<br \/>\nThe given equation represents a linear function<\/p>\n<p>Explanation:<br \/>\nThe given function is:<br \/>\ny = \\(\\frac{3 x}{5}\\)<br \/>\n5y = 3x<br \/>\n3x &#8211; 5y = 0<br \/>\ny = \\(\\frac{3}{5}\\)x + 0<br \/>\nWe know that,<br \/>\nThe standard representation of a linear function is:<br \/>\ny = mx + c<br \/>\nWhen we compare the above function with the standard representation of a linear function,<br \/>\nWe can conclude that the given function is a linear function<\/p>\n<p>Question 7.<br \/>\ny = 5 &#8211; 2x\u00b2<br \/>\nAnswer:<br \/>\nThe given equation represents a non-linear function<\/p>\n<p>Explanation:<br \/>\nThe given function is:<br \/>\ny = 5 &#8211; 2x\u00b2<br \/>\nWe know that,<br \/>\nThe standard representation of a linear function is:<br \/>\ny = mx + c<br \/>\nWhen we compare the given function with the standard representation of a linear function,<br \/>\nWe can conclude that the given function is a non-linear function<\/p>\n<p>Question 8.<br \/>\nThe linear function m = 50 &#8211; 9d represents the amount m (in dollars) of money you have after buying d DVDs.<br \/>\n(a) Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nAnswer:<br \/>\nThe given linear function is:<br \/>\nm = 50 &#8211; 9d<br \/>\nWhere,<br \/>\nm is the amount in dollars you have after buying d DVDs<br \/>\nm is the dependent variable<br \/>\nd is the independent variable<br \/>\nWe know that,<br \/>\nThe domain is defined for the independent variables<br \/>\nSo,<br \/>\nLet<br \/>\nd = 0, 1, 2, 3, 4, 5&#8230;&#8230;<br \/>\nNow,<br \/>\nm = 50 &#8211; 9 (0) = 50<br \/>\nm = 50 &#8211; 9 (1) = 41<br \/>\nm = 50 &#8211; 9 (2) = 32<br \/>\nm = 50 &#8211; 9 (3) = 23<br \/>\nm = 50 &#8211; 9 (4) = 14<br \/>\nm = 50 &#8211; 9 (5) = 5<br \/>\nm = 50 &#8211; 9 (6) = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given linear function is: 0, 1, 2, 3, 4, and 5 [ Since from 6, -ve values are coming and the money will not be -ve ]<br \/>\nThe domain is discrete [ Since a discrete graph is a series of unconnected points ]<\/p>\n<p>(b) Graph the function using its domain.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe domain of the given function is: 0, 1, 2, 3, 4, and 5<br \/>\nHence,<br \/>\nThe representation of the domain in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-12.png\" alt=\"\" width=\"540\" height=\"507\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-12.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-12-300x282.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 9.<br \/>\nIs the domain discrete or continuous? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 40\" width=\"327\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40-300x87.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 40\" width=\"327\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-40-300x87.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nFrom the given table,<br \/>\nThe ordered pairs are:<br \/>\n(1, 12), (2, 24), (3, 36)<br \/>\nHence,<br \/>\nThe representation of the ordered pairs in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-13.png\" alt=\"\" width=\"528\" height=\"513\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-13.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-13-300x291.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\nFrom the above graph,<br \/>\nWe can say that the points are scattered or discrete and they are unconnected<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain for the given table is discrete<\/p>\n<p>Question 10.<br \/>\nA 20-gallon bathtub is draining at a rate of 2.5 gallons per minute. The number g of gallons remaining is a function of the number m of minutes.<br \/>\na. Does this situation represent a linear function? Explain.<br \/>\nAnswer:<br \/>\nIt is given that a 20-gallon bathtub is draining at a rate of 2.5 gallons per minute.<br \/>\nWhere,<br \/>\nThe number g of gallons remaining is a function of the number m of minutes.<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nWe can say that the bathtub is draining at the constant rate<br \/>\nWe know that,<br \/>\nFrom the property of linear function, the change will be constantly increasing or decreasing<br \/>\nSo,<br \/>\nThe representation of the linear function for this situation is:<br \/>\ng = 20 &#8211; 2.5x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given situation is a linear function<\/p>\n<p>b. Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nWe can conclude that the given situation is a linear function<br \/>\nSo,<br \/>\nThe domain of the function = \\(\\frac{Total volume of the bathtub}{The rate of draining}\\)<br \/>\n= \\(\\frac{20}{2.5}\\)<br \/>\n= \\(\\frac{200}{25}\\)<br \/>\n= 8<br \/>\nHence,<br \/>\nThe domain of the function is: 0 \u2264 x \u2264 8 [ Since the draining rate will not be -ve ]<br \/>\nFrom the representation of the domain,<br \/>\nWe can conclude that the domain is continuous<\/p>\n<p>c. Graph the function using its domain.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe linear function is:<br \/>\ng = 20 &#8211; 2.5x<br \/>\nWe know that,<br \/>\nThe domain is: 0 \u2264 x \u2264 8<br \/>\nSo,<br \/>\ng = 20 &#8211; 2.5 (0) = 20<br \/>\ng = 20 &#8211; 2.5 (1) = 17.5<br \/>\ng = 20 &#8211; 2.5 (2) = 15<br \/>\ng = 20 &#8211; 2.5 (3) = 12.5<br \/>\ng = 20 &#8211; 2.5 (4) = 10<br \/>\ng = 20 &#8211; 2.5 (5) = 7.5<br \/>\ng = 20 &#8211; 2.5 (6) = 5<br \/>\ng = 20 &#8211; 2.5 (7) = 2.5<br \/>\ng = 20 &#8211; 2.5 (8) = 0<br \/>\nHence,<br \/>\nThe representation of the linear function using the domain in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-14.png\" alt=\"\" width=\"867\" height=\"505\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-14.png 867w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-14-300x175.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-14-768x447.png 768w\" sizes=\"(max-width: 867px) 100vw, 867px\" \/><\/p>\n<p><b>Write a real-life problem to fit the data shown in the graph. Is the domain of the function discrete or continuous? Explain.<\/b><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-41.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 41\" width=\"199\" height=\"189\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-41.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 41\" width=\"199\" height=\"189\" \/><br \/>\nThe real-life problem that fits the given graph is:<br \/>\nAn escalator moves upwards at a constant rate of 1step\/minute.<br \/>\nSo,<br \/>\nWhat is the rate escalator moves upwards after 8 minutes?<br \/>\nFrom the given graph,<br \/>\nWe can say that the points are connected<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain of the function is continuous<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-42.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 42\" width=\"192\" height=\"185\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-42.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 42\" width=\"192\" height=\"185\" \/><br \/>\nThe real-life problem that fits the given graph is:<br \/>\nIf one company offers to pay you $450 per week and the other offers $10 per hour, and both ask you to work 40 hours per week, which company is offering the better rate of pay?<br \/>\nFrom the graph,<br \/>\nWe can observe that the points are connected<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain is continuous<\/p>\n<h3><a id=\"Linear_Functions_3.2_Exercises\"><\/a>Linear Functions 3.2 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b><br \/>\nA linear equation in two variables is an equation that can be written in the form ________, where m and b are constants.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 1\" width=\"573\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-1.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-1-300x31.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b><br \/>\nCompare linear functions and nonlinear functions.<br \/>\nAnswer:<br \/>\nLinear Function:<br \/>\nA Linear function is a relation between two variables that produces a straight line when graphed.<br \/>\nExample:<br \/>\ny = 2x + 3<br \/>\nNon-Linear Function:<br \/>\nA non-linear function\u00a0is a\u00a0function\u00a0that does\u00a0not\u00a0form a line when graphed.<br \/>\nExample:<br \/>\ny = 6x\u00b3<\/p>\n<p>Question 3.<br \/>\n<b>VOCABULARY<\/b><br \/>\nCompare discrete domains and continuous domains.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 3\" width=\"580\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-3.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-3-300x57.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WRITING<\/b><br \/>\nHow can you tell whether a graph shows a discrete domain or a continuous domain?<br \/>\nAnswer:<br \/>\nA &#8220;Discrete domain&#8221; is a set of input values that consists of only certain numbers in an interval.<br \/>\nA &#8220;continuous domain&#8221; is a set of input values that consists of all numbers in an interval.<br \/>\nSometimes, the set of points that represent the solutions of an equation are distinct, and other times the points are connected.<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201310, determine whether the graph represents a linear or nonlinear function. Explain.<\/b><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-43.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 43\" width=\"132\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 5\" width=\"487\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-5.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-5-300x23.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-44.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 44\" width=\"136\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-44.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 44\" width=\"136\" height=\"139\" \/><br \/>\nFrom the above graph,<br \/>\nBy using the vertical test, there is only one point going through each point and the given graph is a straight line<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a linear function<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-45.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 45\" width=\"137\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 7\" width=\"416\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-7.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-7-300x24.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-46.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 46\" width=\"138\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-46.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 46\" width=\"138\" height=\"140\" \/><br \/>\nFrom the above graph,<br \/>\nBy using the vertical test, each line passes through only one point and the given graph is a straight line<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a linear function<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-47.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 47\" width=\"135\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 9\" width=\"485\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-9.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-9-300x19.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-48.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 48\" width=\"141\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-48.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 48\" width=\"141\" height=\"137\" \/><br \/>\nFrom the above graph,<br \/>\nBy using the vertical test, each line passes through each point and the given graph is not a straight line<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a non-linear function<\/p>\n<p><b>In Exercises 11\u201314, determine whether the table represents a linear or nonlinear function. Explain.<\/b><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-49.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 49\" width=\"200\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 11\" width=\"544\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-11.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-11-300x30.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-50.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 50\" width=\"205\" height=\"73\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-50.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 50\" width=\"205\" height=\"73\" \/><br \/>\nFrom the above table,<br \/>\nThe difference between all the values of x is 2 which is a constant through all the values of x<br \/>\nThe difference between all the values of y is not constant<br \/>\nSince the difference between all the values of y is not constant<br \/>\nThe given table is a non-linear function<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-51.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 51\" width=\"206\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 13\" width=\"587\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-13.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-13-300x30.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-52.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 52\" width=\"208\" height=\"71\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-52.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 52\" width=\"208\" height=\"71\" \/><br \/>\nFrom the above table,<br \/>\nThe difference between all the values of x is +1 throughout all the values of x<br \/>\nThe difference between all the values of y is -15 throughout all the values of y<br \/>\nSince the differences are constant for all the values of x and y,<br \/>\nThe given table is a linear function<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 15 and 16, describe and correct the error in determining whether the table or graph represents a linear function.<\/b><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-53.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 53\" width=\"295\" height=\"216\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 15\" width=\"590\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-15.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-15-300x74.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-54.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 54\" width=\"295\" height=\"211\" \/><br \/>\nAnswer:<br \/>\nBy using the vertical test in the graph,<br \/>\nWe can say that each line passes through one point and the given graph is a straight line<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a linear function<\/p>\n<p><b>In Exercises 17\u201324, determine whether the equation represents a linear or nonlinear function. Explain.<\/b><\/p>\n<p>Question 17.<br \/>\ny = x<sup>2<\/sup> + 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 17\" width=\"578\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-17.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-17-300x29.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 18.<br \/>\ny = 7 &#8211; 3x<br \/>\nAnswer:<br \/>\nThe given equation is a linear function<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ny = 7 &#8211; 3x<br \/>\nCompare the given equation with the standard representation of the given linear function<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is a linear function<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-55.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 55\" width=\"92\" height=\"37\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 19\" width=\"593\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-19.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-19-300x31.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 20.<br \/>\ny = 4x(8 &#8211; x)<br \/>\nAnswer:<br \/>\nThe given equation is not a linear function<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ny = 4x (8 &#8211; x)<br \/>\nso,<br \/>\ny = 4x (8) &#8211; 4x (x)<br \/>\ny = 32x &#8211; 4x\u00b2<br \/>\nCompare the above equation with the standard representation of the linear function<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is not a linear function<\/p>\n<p>Question 21.<br \/>\n2 + \\(\\frac{1}{6}\\) y = 3x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 21\" width=\"560\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-21.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-21-300x74.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 22.<br \/>\ny &#8211; x = 2x &#8211; \\(\\frac{2}{3}\\)y<br \/>\nAnswer:<br \/>\nThe given equation is a linear fraction<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\ny &#8211; x = 2x &#8211; \\(\\frac{2}{3}\\)y<br \/>\nSo,<br \/>\ny + \\(\\frac{2}{3}\\)y = 2x + x<br \/>\n\\(\\frac{3y}{3}\\) + \\(\\frac{2y}{3}\\) = 3x<br \/>\n\\(\\frac{5}{3}\\)y = 3x<br \/>\ny = 3x \u00d7 \\(\\frac{3}{5}\\)<br \/>\ny = \\(\\frac{9}{5}\\)x + 0<br \/>\nCompare the above equation with the standard representation of the linear function<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is a linear function<\/p>\n<p>Question 23.<br \/>\n18x &#8211; 2y = 26<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 23\" width=\"561\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-23.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-23-300x74.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 24.<br \/>\n2x + 3y = 9xy<br \/>\nAnswer:<br \/>\nThe given equation is not a linear fraction<\/p>\n<p>Explanation:<br \/>\nThe given equation is:<br \/>\n2x + 3y = 9xy<br \/>\n2x = 9xy &#8211; 3y<br \/>\n2x = y (9x &#8211; 3)<br \/>\ny = \\(\\frac{2}{9x &#8211; 3}\\)x<br \/>\nCompare the above equation with the standard representation of the linear function<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is not a linear function<\/p>\n<p>Question 25.<br \/>\n<b>CLASSIFYING FUNCTIONS<\/b><br \/>\nWhich of the following equations do not represent linear functions? Explain.<br \/>\nA. 12 = 2x<sup>2<\/sup> + 4y<sup>2<\/sup><br \/>\nB. y &#8211; x + 3 = x<br \/>\nC. x = 8<br \/>\nD. x = 9 &#8211; \\(\\frac{3}{4}\\)y<br \/>\nE. y = \\(\\frac{5x}{11}\\)<br \/>\nF = \\(\\sqrt{x}\\) + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 25\" width=\"559\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-25.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-25-300x124.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 26.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nFill in the table so it represents a linear function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-3-Graphing-Linear-Functions-56.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 3 Graphing Linear Functions 56\" width=\"247\" height=\"71\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-3-Graphing-Linear-Functions-56.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 3 Graphing Linear Functions 56\" width=\"247\" height=\"71\" \/><br \/>\nFrom the above table,<br \/>\nwe can observe that the difference between all the values of x is 5 which is a constant<br \/>\nNow,<br \/>\nTo find the difference between all the values of y which is a constant, we have to use the trial and error method.<br \/>\nNow,<br \/>\nIf we add +1 to -1 and continue adding +1 to all the values of y, then<br \/>\n-1 + 1 = 0<br \/>\n0 + 1 = 1<br \/>\n1 + 1 = 2<br \/>\n2 + 1 = 3<br \/>\nBut the last value is: 11<br \/>\nNow,<br \/>\nIf we add +2 to -1 and continue adding +2 to all the values of y, then<br \/>\n-1 + 2 = 1<br \/>\n1 + 2 = 3<br \/>\n3 + 2 = 5<br \/>\n5 + 2 = 7<br \/>\nBut the last value is: 11<br \/>\nNow,<br \/>\nIf we add +3 to -1 and continue adding +3 to all the values of y, then<br \/>\n-1 + 3 = 2<br \/>\n2 + 3 = 5<br \/>\n5 + 3 = 8<br \/>\n8 + 3 = 11<br \/>\nThe last value is also: 11<br \/>\nHnece, from the above,<br \/>\nWe can conclude that we have to add +3 to make all the values of y constant so that the given table represents a linear function<br \/>\nThe completed table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-17.jpg\" alt=\"\" width=\"237\" height=\"63\" \/><\/p>\n<p><b>In Exercises 27 and 28, find the domain of the function represented by the graph. Determine whether the domain is discrete or continuous. Explain.<\/b><\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-57.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 57\" width=\"158\" height=\"156\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 27\" width=\"536\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-27.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-27-300x35.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-58.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 58\" width=\"163\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-58.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 58\" width=\"163\" height=\"157\" \/><br \/>\nWe know that,<br \/>\nThe domain is defined as the range of all the values of x<br \/>\nSo,<br \/>\nFrom the above graph,<br \/>\nThe domain is: 0, 1, 2, 3, 4, 5, 6, and 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain of the given graph is: 0, 1, 2, 3, 4, 5, 6, and 7<\/p>\n<p><b>In Exercises 29\u201332, determine whether the domain is discrete or continuous. Explain.<\/b><\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-59.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 59\" width=\"223\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 29\" width=\"569\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-29.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-29-300x31.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-60.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 60\" width=\"300\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-60.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 60\" width=\"300\" height=\"91\" \/><br \/>\nFrom the given table,<br \/>\nThe difference between the values of x is 1 which is constant throughout all of the values of x<br \/>\nThe difference between the values of y is 3 which is constant throughout all of the values of y<br \/>\nHence,<br \/>\nSince the difference is constant for both the values of x and y,<br \/>\nThe domain of the given table is continuous<\/p>\n<p><span style=\"font-size: 16px;\">Question 31.<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-61.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 61\" width=\"264\" height=\"93\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 31\" width=\"581\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-31.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-31-300x29.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-62.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 62\" width=\"255\" height=\"101\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-62.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 62\" width=\"255\" height=\"101\" \/><br \/>\nFrom the above table,<br \/>\nThe difference between all the values of x is 1 which is a constant<br \/>\nThe difference between all the values of y is 4 which is a constant<br \/>\nHence,<br \/>\nSince the difference between all the values of x and y is constant,<br \/>\nThe given function is a linear function<br \/>\nThe domain of the given function is continuous<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 33 and 34, describe and correct the error in the statement about the domain. 33. xy214324682.5 is in the domain.<\/b><\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-63.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 63\" width=\"290\" height=\"216\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 33\" width=\"576\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-33.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-33-300x31.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-64.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 64\" width=\"282\" height=\"241\" \/><br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe domain is the range of all the values of x<br \/>\nNow,<br \/>\nFrom the given graph,<br \/>\nThe domain of the given function is: 0, 1, 2, 3, 4, 5, and 6<br \/>\nFrom the given graph,<br \/>\nWe can observe that the domain of the given graph is continuous because there are not any unconnected points in the graph<\/p>\n<p>Question 35.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe linear function m = 55 &#8211; 8.5b represents the amount m (in dollars) of money that you have after buying b books.<br \/>\na. Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nb. Graph the function using its domain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-65.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 65\" width=\"311\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-65.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-65-300x146.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 35.1\" width=\"589\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.1.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.1-300x234.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 35.2\" width=\"569\" height=\"408\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.2.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-35.2-300x215.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe number y of calories burned after x hours of rock climbing is represented by the linear function y = 650x.<br \/>\na. Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nb. Graph the function using its domain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-65.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 65.1\" width=\"148\" height=\"155\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that<br \/>\nThe number y of calories burned after x hours of rock climbing is represented by the linear function<br \/>\ny = 650x.<br \/>\nIt is given that x is the number of hours<br \/>\nHence,<br \/>\nThe domain of the given function is:<br \/>\n1 \u2264 x \u2264 24<br \/>\nSince, the domain of the function is inequality,<br \/>\nThe domain of the function is continuous<\/p>\n<p>b.<br \/>\nThe given function is:<br \/>\ny = 650x<br \/>\nFrom part (a),<br \/>\nThe domain of the function is: 1 \u2264 x \u2264 24<br \/>\nSo,<br \/>\ny = 650 (1) = 650<br \/>\ny = 650 (2) = 1300<br \/>\ny = 650 (3) = 1950<br \/>\n.<br \/>\n.<br \/>\n.<br \/>\n.<br \/>\ny = 650 (12) = 7800<br \/>\nHence,<br \/>\nThe representation of the function with the domain in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-17.png\" alt=\"\" width=\"737\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-17.png 737w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-17-300x208.png 300w\" sizes=\"(max-width: 737px) 100vw, 737px\" \/><\/p>\n<p>Question 37.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou are researching the speed of sound waves in dry air at 86\u00b0F. The table shows the distances d (in miles) sound waves travel in t seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-66.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 66\" width=\"191\" height=\"168\" \/><br \/>\na. Does this situation represent a linear function? Explain.<br \/>\nb. Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nc. Graph the function using its domain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 37\" width=\"569\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-37.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-37-300x195.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function y = 30 + 5x represents the cost y (in dollars) of having your dog groomed and buying x extra services.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-67.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 67\" width=\"282\" height=\"177\" \/><br \/>\na. Does this situation represent a linear function? Explain.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 30 + 5x<br \/>\nWe know that,<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nCompare the given function with the standard representation<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given situation represents a linear function<\/p>\n<p>b. Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 30 + 5x<br \/>\nWhere,<br \/>\ny is the amount in dollars<br \/>\nx is the cost of extra grooming services<br \/>\nFrom the above,<br \/>\nThe maximum number of given extra grooming services is: 5<br \/>\nSo,<br \/>\nWe can use extra grooming service or not<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the given function is: 0 \u2264 x \u2264 5<br \/>\nHence,<br \/>\nThe domain of the given function is continuous<\/p>\n<p>c. Graph the function using its domain.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 30 + 5x<br \/>\nWe know that,<br \/>\nThe domain of the function is: 0 \u2264 x \u2264 5<br \/>\nSo,<br \/>\ny = 30 + 5(0) = 30<br \/>\ny = 30 + 5 (1) = 35<br \/>\ny = 30 + 5(2) = 40<br \/>\ny = 30 + 5 (3) = 45<br \/>\ny = 30 + 5 (4) = 50<br \/>\ny = 30 + 5 (5) = 55<br \/>\nHence,<br \/>\nThe representation of the function using its domain in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-16.png\" alt=\"\" width=\"628\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-16.png 628w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-16-300x246.png 300w\" sizes=\"(max-width: 628px) 100vw, 628px\" \/><\/p>\n<p><b>WRITING In Exercises 39\u201342, write a real-life problem to fit the data shown in the graph. Determine whether the domain of the function is discrete or continuous. Explain.<\/b><\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-68.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 68\" width=\"158\" height=\"162\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 39\" width=\"582\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-39.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-39-300x59.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-69.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 69\" width=\"172\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-69.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 69\" width=\"172\" height=\"169\" \/><br \/>\nFrom the above graph,<br \/>\nThe real-life situation is:<br \/>\nThe temperature of a country in the winter season falls by 2\u00b0C<br \/>\nThe domain of the graph is continuous as there are not any unconnected points<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-70.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 70\" width=\"159\" height=\"162\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 41\" width=\"564\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-41.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-41-300x60.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-71.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 71\" width=\"170\" height=\"159\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-71.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 71\" width=\"170\" height=\"159\" \/><br \/>\nFrom the above graph,<br \/>\nThe real-life situation is:<br \/>\nThe number of ants in a colony increase by 2 times per day. So, the number of ants increases by how many times in 5 days?<br \/>\nThe domain of the given graph is continuous since there is not any unconnected point in the graph<\/p>\n<p>Question 43.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nThe table shows your earnings y (in dollars) for working x hours.<br \/>\na. What is the missing y-value that makes the table represent a linear function?<br \/>\nb. What is your hourly pay rate?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-72.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 72\" width=\"179\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 43\" width=\"568\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-43.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-43-300x65.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nThe linear function d = 50t represents the distance d (in miles) Car A is from a car rental store after t hours. The table shows the distances Car B is from the rental store.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-73.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 73\" width=\"177\" height=\"127\" \/><br \/>\na. Does the table represent a linear or nonlinear function? Explain.<br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-73.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 73\" width=\"177\" height=\"127\" \/><br \/>\nFrom the above table,<br \/>\nThe values of x increases at a constant rate of 2 but the value of y increases by 120 1st time and by 130 2nd time<br \/>\nHence,<br \/>\nWe can observe that for the constant difference of the values of x, there is no constant difference of the values of y<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given table is a linear function<\/p>\n<p>b. Your friend claims Car B is moving at a faster rate. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nThe function represented by car A is:<br \/>\nd = 50t<br \/>\nThe function represented by car B is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-73.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 73\" width=\"177\" height=\"127\" \/><br \/>\nFrom the above functions,<br \/>\nWe can say that the distance traveled by car A increases at a constant rate whereas the distance traveled by car B increases at a random rate<br \/>\nHence, from the above<br \/>\nWe can conclude that the car B is moving at a faster rate when we observe the above table<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 45\u201348, tell whether the volume of the solid is a linear or nonlinear function of the missing dimension(s). Explain.<\/b><\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74\" width=\"127\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 45\" width=\"583\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-45.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-45-300x59.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74.1\" width=\"145\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74.1\" width=\"145\" height=\"133\" \/><br \/>\nFrom the above figure,<br \/>\nWe can observe that the given figure is a prism<br \/>\nWe know that,<br \/>\nThe volume of a prism = Area \u00d7 height<br \/>\n= Length \u00d7 Width \u00d7 Height<br \/>\nSo,<br \/>\nThe volume of a prism (V) =3 \u00d7 b \u00d7 4<br \/>\nV = 12b<br \/>\nCompare the above volume with y = mx + c<br \/>\nSo,<br \/>\nV = 12b + 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation represents a Linear function<\/p>\n<p>Question 47.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74.2\" width=\"116\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 47\" width=\"575\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-47.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-47-300x46.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74.3\" width=\"104\" height=\"148\" \/><br \/>\nAnswer:<br \/>\nThe given figure is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-74.3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 74.3\" width=\"104\" height=\"148\" \/><br \/>\nFrom the above figure,<br \/>\nWe can observe that the given figure is a cone<br \/>\nWe know that,<br \/>\nThe volume of a cone = \\(\\frac{1}{3}\\) \u03c0r\u00b2h<br \/>\nSo,<br \/>\nThe volume of a cone (V) = \\(\\frac{1}{3}\\) \u00d7 \\(\\frac{22}{7}\\) \u00d7 r\u00b2 \u00d7 15<br \/>\nV = 770r\u00b2<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nBut, the given equation is not in the form of y = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation represents a non-linear function<\/p>\n<p>Question 49.<br \/>\n<b>REASONING<\/b><br \/>\nA water company fills two different-sized jugs. The first jug can hold x gallons of water. The second jug can hold y gallons of water. The company fills A jugs of the first size and B jugs of the second size. What does each expression represent? Does each expression represent a set of discrete or continuous values?<br \/>\na. x + y<br \/>\nb. A + B<br \/>\nc. Ax<br \/>\nd. Ax + By<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-75.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 75\" width=\"181\" height=\"175\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 49\" width=\"604\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-49.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-49-300x175.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nYou go to a farmer\u2019s market to buy tomatoes. Graph a function that represents the cost of buying tomatoes. Explain your reasoning.<br \/>\nAnswer:<br \/>\nIt is given that you go to a farmer&#8217;s market to buy tomatoes.<br \/>\nSo,<br \/>\nTo draw the graph that represents the cost of buying tomatoes,<br \/>\nThe required relation is:<br \/>\nCost of tomatoes \u221d Quantity or weight of tomatoes<br \/>\nWe know that,<br \/>\n\u221d represents the direct relation. In a graph, this relation can be represented in a straight line<br \/>\nHence,<br \/>\nThe representation of the relation of cost of buying tomatoes and weight of tomatoes is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-58457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-15.png\" alt=\"\" width=\"329\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-15.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-15-300x276.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Question 51.<br \/>\n<b>CLASSIFYING A FUNCTION<\/b><br \/>\nIs the function represented by the ordered pairs linear or nonlinear? Explain your reasoning.<br \/>\n(0, 2), (3, 14), (5, 22), (9, 38), (11, 46)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 51\" width=\"583\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-51.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-51-300x73.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nYou and your friend go running. The graph shows the distances you and your friend run.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-76.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 76\" width=\"249\" height=\"191\" \/><br \/>\na. Describe your run and your friend\u2019s run. Who runs at a constant rate? How do you know? Why might a person not run at a constant rate?<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-76.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 76\" width=\"249\" height=\"191\" \/><br \/>\nFrom the graph,<br \/>\nThe running represented by you is a straight line<br \/>\nThe running represented by your friend is not a straight line<br \/>\nWe know that,<br \/>\nA straight line has a constant rate<br \/>\nHence, from the above,<br \/>\nWe can conclude that you run at a constant rate and your friend does not run at a constant rate<\/p>\n<p>b. Find the domain of each function. Describe the domains using the context of the problem.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-76.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 76\" width=\"249\" height=\"191\" \/><br \/>\nWe know that,<br \/>\nThe domain is defined as the range of the values of x<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe domain of the function related to you is: 0 \u2264 x \u2264 50<br \/>\nThe domain of the function related to your friend is: 0 \u2264 x \u2264 50<\/p>\n<p><b>WRITING<br \/>\nIn Exercises 53 and 54, describe a real-life situation for the constraints.<\/b><\/p>\n<p>Question 53.<br \/>\nThe function has at least one negative number in the domain. The domain is continuous.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 53\" width=\"565\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-53.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-53-300x46.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 54.<br \/>\nThe function gives at least one negative number as an output. The domain is discrete.<br \/>\nAnswer:<br \/>\nWhen you go on a world tour and for some days, you stayed in Antarctica,<br \/>\nThe temperatures in Antarctica is at a negative temperature around the year and only for some months in the year, the temperature will be positive<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Tell whether x and y show direct variation. Explain your reasoning.<\/b><\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-77.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 77\" width=\"141\" height=\"131\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 55\" width=\"587\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-55.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-55-300x30.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-78.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 78\" width=\"144\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-78.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 78\" width=\"144\" height=\"130\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that it is a straight line and passes through the origin<br \/>\nHence, from the above,<br \/>\nWe can conclude that x and y shows direct variation<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-79.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 79\" width=\"141\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 57\" width=\"546\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-57.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-57-300x29.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p><b>Evaluate the expression when x = 2.<\/b><\/p>\n<p>Question 58.<br \/>\n6x + 8<br \/>\nAnswer:<br \/>\nThe given expression is: 6x + 8<br \/>\nWhen x = 2,<br \/>\n6x + 8 = 6 (2) + 8<br \/>\n= 12 + 8 = 20<br \/>\nHence,<br \/>\nThe value of the expression when x = 2 is: 20<\/p>\n<p>Question 59.<br \/>\n10 &#8211; 2x + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 59\" width=\"310\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-59.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-59-300x126.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 60.<br \/>\n4(x + 2 &#8211; 5x)<br \/>\nAnswer:<br \/>\nThe given expression is: 4 (x + 2 &#8211; 5x)<br \/>\nWhen x = 2,<br \/>\n4 (x + 2 &#8211; 5x) = 4 (2 + 2 &#8211; 5 (2) )<br \/>\n= 4 (4 &#8211; 10 )<br \/>\n= 4 (-6) = -24<br \/>\nHence,<br \/>\nThe value of the expression when x = 2 is: -24<\/p>\n<p>Question 61.<br \/>\n\\(\\frac{x}{2}\\) + 5x &#8211; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.2-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.2 Question 61\" width=\"292\" height=\"184\" \/><\/p>\n<h3><a id=\"Lesson_3.3_Function_Notation\"><\/a>Lesson 3.3 Function Notation<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you use function notation to represent a function?<br \/>\nThe notation f(x), called function notation, is another name for y. This notation is read as \u201cthe value of f at x\u201d or \u201cf of x.\u201d The parentheses do not imply multiplication. You can use letters other than f to name a function. The letters g, h, j, and k are often used to name functions.<\/p>\n<p><b>EXPLORATION 1<br \/>\nMatching Functions with Their Graphs<br \/>\nWork with a partner.<\/b> Match each function with its graph.<br \/>\na. f (x) = 2x &#8211; 3<br \/>\nb. g(x) = -x + 2<br \/>\nc. h(x) = x<sup>2<\/sup> &#8211; 1<br \/>\nd. j(x) = 2x<sup>2<\/sup> &#8211; 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-80.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 80\" width=\"219\" height=\"174\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-81.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 81\" width=\"463\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-81.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-81-300x174.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\na. f (x) = 2x &#8211; 3<br \/>\nb. g(x) = -x + 2<br \/>\nc. h(x) = x<sup>2<\/sup> &#8211; 1<br \/>\nd. j(x) = 2x<sup>2<\/sup> &#8211; 3<br \/>\nNow,<br \/>\na.<br \/>\nThe given equation is:<br \/>\nf(x) = 2x &#8211; 3<br \/>\nSo,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18.png\" alt=\"\" width=\"502\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18-300x285.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph B) matches this equation<br \/>\nb.<br \/>\nThe given equation is:<br \/>\nf(x) = 2x &#8211; 3<br \/>\nSo,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19.png\" alt=\"\" width=\"509\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19-300x281.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph D) matches this equation<br \/>\nc.<br \/>\nThe given equation is:<br \/>\nh(x) = x\u00b2 &#8211; 1<br \/>\nSo,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20.png\" alt=\"\" width=\"508\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20-300x278.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph A) matches this equation<br \/>\nd.<br \/>\nThe given equation is:<br \/>\nj(x) = 2x\u00b2 &#8211; 3<br \/>\nSo,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21.png\" alt=\"\" width=\"483\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21-300x294.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph C) matches this equation<\/p>\n<p><b>EXPLORATION 2<br \/>\nEvaluating a Function<br \/>\nWork with a partner.<\/b> Consider the function<br \/>\nf(x) = -x + 3.<br \/>\nLocate the points (x, f(x)) on the graph. Explain how you found each point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-82.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 82\" width=\"206\" height=\"137\" \/><br \/>\na. (-1, f(-1))<br \/>\nb. (0, f(0))<br \/>\nc. (1, f(1))<br \/>\nd. (2, f(2))<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf(x) = -x + 3<br \/>\nThe graph for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-82.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 82\" width=\"206\" height=\"137\" \/><br \/>\nNow,<br \/>\nThe simplified points are:<br \/>\na.<br \/>\n(-1, f(-1)) = (-1, [-(-1) + 3]) = (-1, 4)<br \/>\nb.<br \/>\n(0, f(0)) = (0, [0 + 3]) = (0, 3)<br \/>\nc.<br \/>\n(1, f(1)) = (1, [-1 + 3]) = (1, 2)<br \/>\nd.<br \/>\n(2, f(2)) = (2, [-2 + 3]) = (2, 1)<br \/>\nSo,<br \/>\nThe simplified points are:<br \/>\n(-1, 4), (0, 3), (1, 2), (2, 1)<br \/>\nHence,<br \/>\nThe representation of the above points in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22.png\" alt=\"\" width=\"521\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22-300x285.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you use function notation to represent a function? How are standard notation and function notation similar? How are they different?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-82.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 82.1\" width=\"304\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-82.1.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-82.1-300x56.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<br \/>\n&#8220;Function notation&#8221; is a simpler method of describing a function without a lengthy written explanation. The most frequently used function notation is f(x) which is read as \u201cf\u201d of \u201cx\u201d.<br \/>\nThe standard notation and function notation are similar in the way of simplification<br \/>\nDifference betwwen Function notataion and standard notation:<br \/>\nThe representation of function notation largely depends on the number of variables present in the function<br \/>\nEx:<br \/>\nf(x,y) = 2xy + 3<br \/>\nf(x) = x + 3<br \/>\nThe representation of the standard notation does not depend on the number of variables present in the equation.<\/p>\n<p><b>3.3 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Evaluate the function when x = \u22124, 0, and 3.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = 2x &#8211; 5<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf(x) = 2x &#8211; 5<br \/>\nNow,<br \/>\nWhen x = -4,<br \/>\nf(-4) = 2 (-4) &#8211; 5 = -8 &#8211; 5 = -13<br \/>\nWhen x = 0,<br \/>\nf(0) = 2 (0) &#8211; 5 = 0 &#8211; 5 = -5<br \/>\nWhen x = 3,<br \/>\nf(3) = 2 (3) &#8211; 5 = 6 &#8211; 5 = 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of f(x) when x = -4, 0, 3 are: -13, -5, and 1<\/p>\n<p>Question 2.<br \/>\ng(x) = -x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ng(x) = -x &#8211; 1<br \/>\nNow,<br \/>\nWhen x = -4,<br \/>\ng(-4) = -[-4] &#8211; 1 = 4 &#8211; 1 = 3<br \/>\nWhen x = 0,<br \/>\ng(0) = 0 &#8211; 1 = -1<br \/>\nWhen x = 3,<br \/>\ng(3) = -3 &#8211; 1 = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of g(x) when x = -4, 0, 3 are: 3, -1, and -4<\/p>\n<p>Question 3.<br \/>\n<b>WHAT IF?<\/b> In Example 2, let f(t) be the outside temperature (\u00b0F) t hours after 9 A.M. Explain the meaning of each statement.<br \/>\na. f(4) = 75<br \/>\nb. f(m) = 70<br \/>\nc. f(2) = f(9)<br \/>\nd. f(6) &gt; f(0)<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Find the value of x so that the function has the given value.<\/b><\/p>\n<p>Question 4.<br \/>\nf(x) = 6x + 9; f(x) = 21<br \/>\nAnswer:<br \/>\nThe value of x is: 2<\/p>\n<p>Explanation:<br \/>\nThe give function is:<br \/>\nf(x) = 6x + 9 with f(x) = 21<br \/>\nSo,<br \/>\n21 = 6x + 9<br \/>\n6x = 21 &#8211; 9<br \/>\n6x = 12<br \/>\nx = 12 \/ 6<br \/>\nx = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x in the given function is: 2<\/p>\n<p>Question 5.<br \/>\ng(x) = \\(-\\frac{1}{2}\\)x + 3; g(x) = -1<br \/>\nAnswer:<br \/>\nThe value of x is: 8<\/p>\n<p>Explanation:<br \/>\nThe given function is:<br \/>\ng(x) = \\(-\\frac{1}{2}\\)x + 3 with g(x) = -1<br \/>\nSo,<br \/>\n-1 = \\(-\\frac{1}{2}\\)x + 3<br \/>\n\\(-\\frac{1}{2}\\)x = -1 &#8211; 3<br \/>\n\\(-\\frac{1}{2}\\)x = -4<br \/>\n&#8211;\\(\\frac{1}{2}\\)x = -4<br \/>\n\\(\\frac{1}{2}\\)x = 4<br \/>\nx = 2(4)<br \/>\nx = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of x in the given function is: 8<\/p>\n<p><b>Graph the linear function.<\/b><\/p>\n<p>Question 6.<br \/>\nf(x) = 3x &#8211; 2<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf(x) = 3x &#8211; 2<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nf(-2) = 3 (-2) &#8211; 2 = -6 &#8211; 2 = -8<br \/>\nf(-1) = 3(-1) &#8211; 2 = -3 &#8211; 2 = -5<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18.jpg\" alt=\"\" width=\"406\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18.jpg 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-18-300x62.jpg 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23.png\" alt=\"\" width=\"478\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23-300x296.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 7.<br \/>\ng(x) = -x + 4<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ng(x) = -x + 4<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\ng(-2) = -[-2] + 4 = 2 + 4 = 6<br \/>\ng(-1) = -[-1] + 4 = 4 + 1 = 5<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19.jpg\" alt=\"\" width=\"403\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19.jpg 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-19-300x63.jpg 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24.png\" alt=\"\" width=\"488\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24-300x293.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 8.<br \/>\nh(x) = \\(-\\frac{3}{4}\\)x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nh(x) = \\(-\\frac{3}{4}\\)x &#8211; 1<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nh(-2) = \\(-\\frac{3}{4}\\) (-2) &#8211; 1<br \/>\n= \\(\\frac{3}{2}\\) &#8211; 1<br \/>\n= \\(\\frac{1}{2}\\)<br \/>\nh(-1) = \\(-\\frac{3}{4}\\) (-1) &#8211; 1<br \/>\n= \\(\\frac{3}{4}\\) &#8211; 1<br \/>\n= \\(-\\frac{1}{4}\\)<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20.jpg\" alt=\"\" width=\"404\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20.jpg 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-20-300x62.jpg 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25.png\" alt=\"\" width=\"489\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25-300x292.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 9.<br \/>\n<b>WHAT IF?<\/b><br \/>\nLet f(x) = 250 &#8211; 75x represent the second flight, where f(x) is the number of miles the helicopter is from its destination after x hours. Which flight takes less time? Explain.<\/p>\n<h3><a id=\"Function_Notation_3.3_Exercises\"><\/a>Function Notation 3.3 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE <\/b><br \/>\nWhen you write the function y = 2x + 10 as f(x) = 2x + 10, you are using ______________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 1\" width=\"577\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-1-300x31.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>REASONING <\/b><br \/>\nYour height can be represented by a function h, where the input is your age. What does h(14) represent?<br \/>\nAnswer:<br \/>\nIt is given that your height can be represented by a function h, where the input is your age<br \/>\nSo,<br \/>\nh (14) means you are 14 years old<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201310, evaluate the function when x = \u20132, 0, and 5.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 3\" width=\"195\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-3.png 195w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-3-192x300.png 192w\" sizes=\"(max-width: 195px) 100vw, 195px\" \/><\/p>\n<p>Question 4.<br \/>\ng(x) = 3x<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ng (x) = 3x<br \/>\nWhen x = -2,<br \/>\ng (-2) = 3 (-2) = -6<br \/>\nWhen x = 0,<br \/>\ng (0) = 3 (0) = 0<br \/>\nWhen x = 5,<br \/>\ng (5) = 3 (5) = 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of g (x) when x = -2, 0, 5 is: -6, 0, and 15<\/p>\n<p>Question 5.<br \/>\nh(x) = -2x + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 5\" width=\"256\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-5.png 256w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-5-187x300.png 187w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>Question 6.<br \/>\nr(x) = -x &#8211; 7<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nr (x) = -x &#8211; 7<br \/>\nWhen x = -2,<br \/>\nr (-2) = -[-2] &#8211; 7<br \/>\n= 2 &#8211; 7 = -5<br \/>\nWhen x = 0,<br \/>\nr (0) = 0 &#8211; 7 = -7<br \/>\nWhen x = 5,<br \/>\nr (5) = -5 &#8211; 7 = -12<br \/>\nHence, from the above,<br \/>\nWe can conclude taht the values of r (x) when x = 0, -2, 5 is: -5, -7, and -12<\/p>\n<p>Question 7.<br \/>\np(x) = -3 + 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 7\" width=\"253\" height=\"407\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-7.png 253w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-7-186x300.png 186w\" sizes=\"(max-width: 253px) 100vw, 253px\" \/><\/p>\n<p>Question 8.<br \/>\nb(x) = 18 &#8211; 0.5x<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nb (x) = 18 &#8211; 0.5x<br \/>\nWhen x = -2,<br \/>\nb (-2) = 18 &#8211; 0.5 (-2)<br \/>\n= 18 + 1 = 19<br \/>\nWhen x = 0,<br \/>\nb (0) = 18 &#8211; 0.5 (0) = 18<br \/>\nWhen x = 5,<br \/>\nb (5) = 18 &#8211; 0.5 (5)<br \/>\n18 &#8211; 2.5 = 15.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of b (x) when x = 0, -2, 5 is: 19, 18, and 15.5<\/p>\n<p>Question 9.<br \/>\nv(x) = 12 &#8211; 2x &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 9\" width=\"270\" height=\"551\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-9.png 270w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-9-147x300.png 147w\" sizes=\"(max-width: 270px) 100vw, 270px\" \/><\/p>\n<p>Question 10.<br \/>\nn(x) = -1 &#8211; x + 4<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nn (x) = -1 &#8211; x + 4<br \/>\nWhen x = -2,<br \/>\nn (-2) = -1 &#8211; [-2] + 4<br \/>\n= -1 + 2 + 4<br \/>\n= 6 &#8211; 1<br \/>\n= 5<br \/>\nWhen x = 0,<br \/>\nn (0) = -1 &#8211; 0 + 4<br \/>\n= -1 + 4 = 3<br \/>\nWhen x = 2,<br \/>\nn (2) = -1 &#8211; 2 + 4<br \/>\n= 4 &#8211; 3<br \/>\n= 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of n (x) when x = -2, 0, 5 is: 5, 3, and 1<\/p>\n<p>Question 11.<br \/>\n<b>INTERPRETING FUNCTION NOTATION<\/b><br \/>\nLet c(t) be the number of customers in a restaurant t hours after 8 A.M. Explain the meaning of each statement.<br \/>\na. c(0) = 0<br \/>\nb. c(3) = c(8)<br \/>\nc. c(n) = 29<br \/>\nd. c(13) &lt; c(12)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 11\" width=\"595\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-11.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-11-300x180.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Question 12.<br \/>\n<b>INTERPRETING FUNCTION NOTATION<br \/>\n<\/b>Let H(x) be the percent of U.S. households with Internet use x years after 1980. Explain the meaning of each statement.<br \/>\na. H(23) = 55<br \/>\nb. H(4) = k<br \/>\nc. H(27) \u2265 61<br \/>\nd. H(17) + H(21) \u2248 H(29)<br \/>\nAnswer:<br \/>\nIt is given that H (x) is the percent of U.S households with internet use x years after 1980<br \/>\nNow,<br \/>\na.<br \/>\nThe given function is:<br \/>\nH (23) = 55<br \/>\nThe meaning of the above function is:<br \/>\n23 years after 1980, 55% of U.S households will be using the internet<\/p>\n<p>b.<br \/>\nThe given function is:<br \/>\nH(4) = k<br \/>\nThe meaning of the above function is:<br \/>\n4 years after 1980, k% of U.S households will be using the internet<\/p>\n<p>c.<br \/>\nThe given function is:<br \/>\nH(27) \u2265 61<br \/>\nThe meaning of the above function is:<br \/>\n27 years after 1980, more than 61% of U.S households will be using the internet<\/p>\n<p>d.<br \/>\nThe given function is:<br \/>\nH(17) + H(21) \u2248 H(29)<br \/>\nThe meaning of the above function is:<br \/>\nThe percentage of U.S households using the internet after 29 years is equal to the sum of percentage of household using the internet after 17 years and 21 years<\/p>\n<p><b>In Exercises 13\u201318, find the value of x so that the function has the given value.\u00a0\u00a0<\/b><\/p>\n<p>Question 13.<br \/>\nh(x) = -7x; h(x) = 63<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 13\" width=\"248\" height=\"198\" \/><\/p>\n<p>Question 14.<br \/>\nt(x) = 3x; t(x) = 24<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nt (x) = 3x with t (x) = 24<br \/>\nSo,<br \/>\n24 = 3x<br \/>\nx = 24 \/ 3<br \/>\nx = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 8<\/p>\n<p>Question 15.<br \/>\nm(x) = 4x + 15; m(x) = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 15\" width=\"248\" height=\"265\" \/><\/p>\n<p>Question 16.<br \/>\nk(x) = 6x &#8211; 12; k(x) = 18<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nk (x) = 6x &#8211; 12 with k (x) = 18<br \/>\nSo,<br \/>\n6x &#8211; 12 = 18<br \/>\n6x = 12 + 18<br \/>\n6x = 30<br \/>\nx = 30 \/ 6<br \/>\nx = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 5<\/p>\n<p>Question 17.<br \/>\nq(x) = \\(\\frac{1}{2}\\)x &#8211; 3; q(x) = -4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 17\" width=\"256\" height=\"270\" \/><\/p>\n<p>Question 18.<br \/>\nj(x) = &#8211;\\(\\frac{4}{5}\\)x + 7; j(x) = -5<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nj (x) = &#8212;\\(\\frac{4}{5}\\)x + 7 with j (x) = -5<br \/>\nSo,<br \/>\n-5 = &#8211;\\(\\frac{4}{5}\\)x + 7<br \/>\n-5 &#8211; 7 = &#8211;\\(\\frac{4}{5}\\)x<br \/>\n&#8211;\\(\\frac{4}{5}\\)x = -12<br \/>\n\\(\\frac{4}{5}\\)x = 12<br \/>\nx = 12 \u00d7 &#8211;\\(\\frac{5}{4}\\)<br \/>\nx = 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 15<\/p>\n<p><b>In Exercises 19 and 20, find the value of x so that f(x) = 7.\u00a0<\/b><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-83.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 83\" width=\"144\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 19\" width=\"464\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-19.png 464w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-19-300x23.png 300w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-84.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 84\" width=\"137\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf (x) = 7<br \/>\nSo,<br \/>\nWe know that,<br \/>\ny = f (x)<br \/>\nSo,<br \/>\nFrom the above,<br \/>\nWe can say that the value of y is: 7<br \/>\nNow,<br \/>\nTo find the value of x, observe the location corresponding to the value of y<br \/>\nSo,<br \/>\nThe value of x is: -2<br \/>\nHence,<br \/>\nThe point of the graph where f (x) = 7 is: (-2, 7)<\/p>\n<p>Question 21.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function C(x) = 17.5x &#8211; 10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.<br \/>\na. How much does it cost to buy five tickets?<br \/>\nb. How many tickets can you buy for $130?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 21\" width=\"366\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-21.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-21-250x300.png 250w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function d(t) = 300,000t represents the distance (in kilometers) that light travels in t seconds.<br \/>\na. How far does light travel in 15 seconds?<br \/>\nb. How long does it take light to travel 12 million kilometers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-85.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 85\" width=\"166\" height=\"214\" \/><br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nd (t) = 300,000t<br \/>\nrepresents the distance in kilometers that travels in t seconds<br \/>\na.<br \/>\nThe distance traveled by light in 15 seconds is:<br \/>\nd (15) = 300,000 (15)<br \/>\n= 4,500,000 kilometers<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance traveled by light in 15 seconds is: 4,500,000 kilometers<\/p>\n<p>b.<br \/>\nIt is given that the total distance traveled by light is 12 million kilometers<br \/>\nSo,<br \/>\nd (t) = 12 million kilometers<br \/>\nSo,<br \/>\n12,000,000 = 300,000 (t)<br \/>\nt = 12,000,000 \/ 300,000<br \/>\nt = 40 seconds<br \/>\nHence, from the above,<br \/>\nWe can conclude that the time taken by light to travel 12 million kilometers is: 40 seconds<\/p>\n<p><b>In Exercises 23\u201328, graph the linear function.\u00a0<\/b><\/p>\n<p>Question 23.<br \/>\np(x) = 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 23\" width=\"289\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-23.png 289w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-23-260x300.png 260w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/p>\n<p>Question 24.<br \/>\nh(x) = -5<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nh (x) = -5<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) to plot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21.jpg\" alt=\"\" width=\"403\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21.jpg 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-21-300x64.jpg 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29.png\" alt=\"\" width=\"479\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29-300x296.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 25.<br \/>\nd(x) = \\(-\\frac{1}{2} x\\) &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 25\" width=\"341\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-25.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-25-300x248.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 26.<br \/>\nw(x) = \\(\\frac{3}{5} x\\) + 2<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nw (x) = \\(\\frac{3}{5} x\\) + 2<br \/>\nSo,<br \/>\nw (x) = \\(\\frac{3}{5}\\) x + 2<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) to plot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22.jpg\" alt=\"\" width=\"403\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22.jpg 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-22-300x65.jpg 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30.png\" alt=\"\" width=\"512\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30-300x275.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 27.<br \/>\ng(x) = -4 + 7x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 27\" width=\"353\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-27.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-27-300x282.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = 3 &#8211; 6x<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf (x) = 3 &#8211; 6x<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) to plot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23.jpg\" alt=\"\" width=\"402\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-23-300x62.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31.png\" alt=\"\" width=\"487\" height=\"466\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31-300x287.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 29.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nThe graph shows the percent p(in decimal form) of battery power remaining in a laptop computer after t hours of use. A tablet computer initially has 75% of its battery power remaining and loses 12.5% per hour. Which computer\u2019s battery will last longer? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-86.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 86\" width=\"194\" height=\"187\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 29.1\" width=\"566\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.1.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.1-300x244.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 29.2\" width=\"603\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.2.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-29.2-300x188.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 30.<br \/>\n<b>PROBLEM-SOLVING<\/b><br \/>\nThe function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is the number of hours of labor. The table shows sample labor costs from its main competitor, Master Remodeling. The deck is estimated to take 8 hours of labor. Which company would you hire? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-87.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 87\" width=\"110\" height=\"111\" \/><br \/>\nAnswer:<br \/>\nIt is given that the given function<br \/>\nC(x) = 25x + 50<br \/>\nrepresents the labor cost (in dollars) for certified Remodeling to build a deck<br \/>\nWhere,<br \/>\nx is the number of hours of labor.<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-87.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 87\" width=\"110\" height=\"111\" \/><br \/>\nThe given table shows the sample labor costs from its main competitor, Master Remodeling.<br \/>\nIt is also given that the deck is estimated to take 8 hours of labor.<br \/>\nNow,<br \/>\nFrom the given table,<br \/>\nWe can observe that the competitor &#8216;Master Remodeling&#8217; completes the deck in 6 hours whereas for certified Remodeling, it will take 8 hours of labor to complete a deck thereby increases the cost. i.e., the avlue of C(x) also increases when compared to the Master Remodeling<br \/>\nHence, from the above,<br \/>\nWe can conclude that we choose &#8220;Master Remodeling&#8221; company<\/p>\n<p>Question 31.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nLet P(x) be the number of people in the U.S. who own a cell phone x years after 1990. Your friend says that P(x + 1) &gt; P(x) for any x because x + 1 is always greater than x. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 31\" width=\"587\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-31.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-31-300x42.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nLet B(t) be your bank account balance after t days. Describe a situation in which B(0) &lt; B(4) &lt; B(2).<br \/>\nAnswer:<br \/>\nThe given relation is:<br \/>\nB (0) &lt; B (4) &lt; B (2)<br \/>\nLet us consider<br \/>\nSunday &#8211; Day 0<br \/>\nMonday -Day 1<br \/>\nTuesday -Day 2<br \/>\nWednesday &#8211; Day 3<br \/>\nThursday &#8211; Day 4<br \/>\nFriday &#8211; Day 5<br \/>\nSaturday &#8211; Day 6<br \/>\nNow,<br \/>\nBy using the above relation,<br \/>\nThe situation we can assume is:<br \/>\nA man named A works at a company where he receives his salary every Tuesday (Day 2) of a normal week. He then spends some of his salary paying bills on Thursday (Day 4). On Sunday, he decides to spend all of his remaining salary on food, groceries, and transportation allowance for the following week<\/p>\n<p>Question 33.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nRewrite each geometry formula using function notation. Evaluate each function when r = 5 feet. Then explain the meaning of the result.<br \/>\na. Diameter, d = 2r<br \/>\nb. Area, A = \u03c0r<sup>2<\/sup><br \/>\nc. Circumference, C = 2\u03c0r<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-88.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 88\" width=\"116\" height=\"103\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 33\" width=\"604\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-33.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-33-300x234.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe function y = A(x) represents the attendance at a high school x weeks after a flu outbreak. The graph of the function is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\na. What happens to the school\u2019s attendance after the flu outbreak?<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\nFrom the above graph,<br \/>\nWe can observe that after the flu outbreak, the school&#8217;s attendance first decreased and then again steadily increased<\/p>\n<p>b. Estimate A(13) and explain its meaning.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\nNow,<br \/>\nWe know that<br \/>\nThe function notation and the standard notations are similar<br \/>\nSo,<br \/>\ny = A (x)<br \/>\nSo,<br \/>\ny = A (13)<br \/>\nSo,<br \/>\nThe value of x is: 13<br \/>\nTo find the value of y or the given function, observe the graph for the value of y corresponding to the value of x i.e., 13<br \/>\nSo,<br \/>\nFrom the graph,<br \/>\ny = 430 [Approximately]<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe estimation of A(13) is:<br \/>\nA (13) = 430 {Approximately]<\/p>\n<p>c. Use the graph to estimate the solution(s) of the equation A(x) = 400. Explain the meaning of the solution(s).<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\nThe given equation is:<br \/>\nA (x) = 400<br \/>\nFrom the above graph,<br \/>\nFor the solution of the given equation i.e., the value of x,<br \/>\nObserve the location of 400 in the graph and its corresponding x-value<br \/>\nHence,<br \/>\nFrom the graph,<br \/>\nWe can observe that the value of x is: 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution of the given equation is: 1<\/p>\n<p>d. What was the least attendance? When did that occur?<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\nFrom the above graph,<br \/>\nWe can observe that there is deep depreciation in the attendance i.e., least attendance of the students in a week<br \/>\nSo,<br \/>\nBy observing the graph,<br \/>\nWe can say that<br \/>\nThe least attendance of the students occurs in the 4th week<br \/>\nThe least attendance of the students is: 350<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe week that has the least attendance is: 4th week<br \/>\nThe number of students of the least attendance is: 350students<\/p>\n<p>e. How many students do you think are enrolled at this high school? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-89.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 89\" width=\"211\" height=\"228\" \/><br \/>\nFrom the given graph,<br \/>\nWe can observe that the y-axis represents the number of students enrolled in the high school<br \/>\nSo,<br \/>\nThe highest number on the y-axis represents the total number of students enrolled in the high school<br \/>\nHence, from the above,<br \/>\nWe can conclude that the total number of students in the high school is: 450 students<\/p>\n<p>Question 35.<br \/>\n<b>INTERPRETING FUNCTION NOTATION<\/b><br \/>\nLet f be a function. Use each statement to find the coordinates of a point on the graph of f.<br \/>\na. f(5) is equal to 9.<br \/>\nb. A solution of the equation f(n) = -3 is 5.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 35\" width=\"581\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-35.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-35-300x65.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>REASONING<\/b><br \/>\nGiven a function f, tell whether the statement f(a + b) = f(a) + f(b) is true or false for all inputs a and b. If it is false, explain why.<br \/>\nAnswer:<br \/>\nLet the given function is:<br \/>\nf or f(x) = mx + c<br \/>\nNow,<br \/>\nLet the values of a and b be integers<br \/>\nSo,<br \/>\nLet,<br \/>\na = 0 and b = 1<br \/>\nSo,<br \/>\nf( a + b ) = f (1)<br \/>\nSo,<br \/>\nf(1) = m + c<br \/>\nNow,<br \/>\nf(a) = f (0) = c<br \/>\nf (b) = f(1) = m + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nf (a + b) is not equal to f (a) + f(b)<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the inequality. Graph the solution. <\/b>(Section 2.5)<\/p>\n<p>Question 37.<br \/>\n-2 \u2264 x &#8211; 11 \u2264 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 37\" width=\"266\" height=\"202\" \/><\/p>\n<p>Question 38.<br \/>\n5a &lt; -35 or a &#8211; 14 &gt; 1<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n5a &lt; -35 or a &#8211; 14 &gt; 1<br \/>\nSo,<br \/>\na &lt; -35 \/ 5 or a &gt; 1 + 14<br \/>\na &lt; -7 or a &gt; 15<br \/>\nHence,<br \/>\nThe solutions of the given inequality are:<br \/>\na &lt; -7 or a &gt; 15<br \/>\nThe representation of the solution of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26.png\" alt=\"\" width=\"576\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26-300x70.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 39.<br \/>\n-16 &lt; 6k + 2 &lt; 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 39\" width=\"301\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-39.png 301w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-39-258x300.png 258w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/><\/p>\n<p>Question 40.<br \/>\n2d + 7 &lt; -9 or 4d &#8211; 1 &gt; -3<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n2d + 7 &lt; -9 or 4d &#8211; 1 &gt; -3<br \/>\n2d &lt; -9 &#8211; 7 or 4d &gt; -3 + 1<br \/>\n2d &lt; -16 or 4d &gt; -2<br \/>\nd &lt; -16 \/ 2 or d &gt; -2 \/ 4<br \/>\nd &lt; -8 or d &gt; -1 \/\u00a0 2<br \/>\nHence,<br \/>\nThe solutions of the given inequality are:<br \/>\nd &lt; -8 or d &gt; -1 \/ 2<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.png\" alt=\"\" width=\"568\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27-300x87.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 41.<br \/>\n5 \u2264 3y + 8 &lt; 17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.3 Question 41\" width=\"268\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-41.png 268w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.3-Question-41-264x300.png 264w\" sizes=\"(max-width: 268px) 100vw, 268px\" \/><\/p>\n<p>Question 42.<br \/>\n4v + 9 \u2264 5 or -3v \u2265 -6<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4v + 9 \u22645 or -3v \u2265 -6<br \/>\nSo,<br \/>\n4v \u2264 5 &#8211; 9 or 3v \u2265 6<br \/>\n4v \u2264 -4 or v \u2265 6 \/ 3<br \/>\nv \u2264 -4 \/ 4 or v \u2265 2<br \/>\nv \u2264 -1 or v \u2265 2<br \/>\nHence,<br \/>\nThe solutions of the given inequality are:<br \/>\nv \u2264 -1 or v \u2265 2<br \/>\nThe representation of the solutions of the given inequality is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-59490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-28.png\" alt=\"\" width=\"583\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-28.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-28-300x74.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Functions_Study_Skills:_Staying_Focused_During_Class\"><\/a>Graphing Linear Functions Study Skills: Staying Focused During Class<\/h3>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-90.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 90\" width=\"655\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-90.png 655w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-90-300x64.png 300w\" sizes=\"(max-width: 655px) 100vw, 655px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 3.1<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-91.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 91\" width=\"617\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-91.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-91-300x23.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><\/p>\n<p><b>Section 3.2<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-92.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 92\" width=\"590\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-92.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-92-300x25.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p><b>Section 3.3<\/b><br \/>\nUsing FunctionNotation, p. 122<\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow can you use technology to confirm your answers in Exercises 40\u201343 on page 110?<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nBy using the above properties,<br \/>\nWe can find the domain and the range of the given Exercises<br \/>\nHence,<br \/>\nWe can confirm the answers in Exercises 40 &#8211; 43 on page 110<\/p>\n<p>Question 2.<br \/>\nHow can you use patterns to solve Exercise 43 on page 119?<br \/>\nAnswer:<br \/>\nIn Exercise 43 on page 119,<br \/>\nWe can observe from the table that the difference between the values of x and y is constant<br \/>\nSo,<br \/>\nBy using the above property, we can find the constant difference between the values of x and y to complete the pattern<\/p>\n<p>Question 3.<br \/>\nHow can you make sense of the quantities in the function in Exercise 21 on page 125?<br \/>\nAnswer:<br \/>\nIn Exercise 21 on page 125,<br \/>\nCompare the given function with the standard representation of the linear function y = mx + c<br \/>\nSo,<br \/>\nIn the above function,<br \/>\nWe know that,<br \/>\nm is the cost of x tickets in dollars<br \/>\nc is the constant<br \/>\nf (x) or y is the function notation of Cost function<\/p>\n<p><b>Study Skills<\/b><\/p>\n<p><b>Staying Focused during Class<\/b><\/p>\n<p>As soon as class starts, quickly review your notes from the previous class and start thinking about math.<br \/>\nRepeat what you are writing in your head.<br \/>\nWhen a particular topic is difficult, ask for another example.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-94.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 94\" width=\"383\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-94.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-94-300x218.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Functions_3.1_-_3.3_Quiz\"><\/a>Graphing Linear Functions 3.1 &#8211; 3.3 Quiz<\/h3>\n<p><b>Determine whether the relation is a function. Explain. <\/b>(Section 3.1)<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-95.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 95\" width=\"290\" height=\"71\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-95.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 95\" width=\"290\" height=\"71\" \/><br \/>\nWe know that for a relationship to be a function,<br \/>\nEach input value has to match with each output value<br \/>\nHence,<br \/>\nFrom the above table,<br \/>\nWe can conclude that the given table is a function since each input value matches with each output value<\/p>\n<p>Question 2.<br \/>\n(-10, 2), (-8, 3), (-6, 5), (-8, 8), (-10, 6)<br \/>\nAnswer:<br \/>\nThe given ordered pairs are:<br \/>\n(-10, 2), (-8, 3), (-6, 5), (-8, 8), (-10, 6)<br \/>\nWe know that,<br \/>\nA relation is said to be a function if each input matches with only 1 output<br \/>\nSo,<br \/>\nBy observing the above-ordered pairs,<br \/>\nWe can say that the input -8 comes 2 times<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given ordered pairs do not represent a function<\/p>\n<p><b>Find the domain and range of the function represented by the graph. <\/b>(Section 3.1)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-96.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 96\" width=\"139\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-96.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 96\" width=\"139\" height=\"136\" \/><br \/>\nWe know that,<br \/>\nThe domain is the set of all x-values<br \/>\nThe range is the set of all y-values<br \/>\nSo,<br \/>\nThe domain of the given graph is: {0, 1, 2, 3, 4}<br \/>\nThe range of the given graph is: {1, -1, -3}<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-97.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 97\" width=\"138\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-97.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 97\" width=\"138\" height=\"137\" \/><\/p>\n<p>We know that,<br \/>\nThe domain is the set of all x-values<br \/>\nThe range is the set of all y-values<br \/>\nSo,<br \/>\nThe domain of the given graph is: {-1, -2, 1, 2}<br \/>\nThe range of the given graph is: {-2, -1, 0, 1, 2}<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-98.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 98\" width=\"136\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-98.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 98\" width=\"136\" height=\"139\" \/><br \/>\nWe know that,<br \/>\nThe domain is the set of all x-values<br \/>\nThe range is the set of all y-values<br \/>\nSo,<br \/>\nThe domain of the given graph is: {-3, -2, -1, 1, 2, 3}<br \/>\nThe range of the given graph is: {-1, 0, 1, 2, 3}<\/p>\n<p><b>Determine whether the graph, table, or equation represents a linear or nonlinear function. Explain. <\/b>(Section 3.2)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-99.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 99\" width=\"145\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-99.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 99\" width=\"145\" height=\"136\" \/><br \/>\nWe know that,<br \/>\nA linear function must always represent a straight line irrespective of the straight line passes through the origin or passes through any other point<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a linear function<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-100.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 100\" width=\"115\" height=\"121\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-100.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 100\" width=\"115\" height=\"121\" \/><br \/>\nThe representation of the values of x and y in the table in the form of ordered pairs is:<br \/>\n(-5, 3), (0, 7), and (5, 10)<br \/>\nRepresent the ordered pairs in the coordinate plane<br \/>\nThe representation of the ordered pairs in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-32.png\" alt=\"\" width=\"495\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-32.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-32-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-32-150x150.png 150w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nFrom the above points, we can say it forms a straight line<br \/>\nA linear function must always represent a straight line irrespective of the straight line passes through the origin or passes through any other point<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given table represents a linear function<\/p>\n<p>Question 8.<br \/>\ny = x(2 &#8211; x)<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = x (2 &#8211; x)<br \/>\nSo,<br \/>\ny = 2 (x) &#8211; x (x)<br \/>\ny = 2x &#8211; x\u00b2<br \/>\nCompare the above function with the standard representation of the linear function<br \/>\nThe standard representation of the linear function is:<br \/>\ny = mx + c<br \/>\nHence, from the above comparison,<br \/>\nWe can conclude that the given function is a non-linear function<\/p>\n<p><b>Determine whether the domain is discrete or continuous. Explain. <\/b>(Section 3.2)<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-101.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 101\" width=\"260\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-101.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 101\" width=\"260\" height=\"69\" \/><br \/>\nFrom the above table,<br \/>\nThe values of x have specific values of y<br \/>\nWe know that,<br \/>\nThe domain is defined as the set of all the values of x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain of the given table is discrete<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-102.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 102\" width=\"246\" height=\"64\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-102.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 102\" width=\"246\" height=\"64\" \/><br \/>\nFrom the above table<br \/>\nWe can observe that the values of x have specific values of y<br \/>\nWe know that,<br \/>\nThe domain is defined as the set of all the values of x<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain of the given table is discrete<\/p>\n<p>Question 11.<br \/>\nFor w(x) = -2x + 7, find the value of x for which w(x) = -3. (Section 3.3)<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nw (x) = -2x + 7 with w (x)\u00a0 = -3<br \/>\nSo,<br \/>\n-3 = -2x + 7<br \/>\n-2x = -3 &#8211; 7<br \/>\n-2x = -10<br \/>\n2x = 10<br \/>\nx = 10 \/ 5<br \/>\nx = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 2<\/p>\n<p><b>Graph the linear function. <\/b>( Section 3.3)<\/p>\n<p>Question 12.<br \/>\ng(x) = x + 3<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ng (x) = x + 3<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24.jpg\" alt=\"\" width=\"402\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-24-300x66.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-33.png\" alt=\"\" width=\"488\" height=\"459\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-33.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-33-300x282.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 13.<br \/>\np(x) = -3x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\np (x) = -3x &#8211; 1<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) toplot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25.jpg\" alt=\"\" width=\"402\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-25-300x62.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-34.png\" alt=\"\" width=\"475\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-34.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-34-300x296.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 14.<br \/>\nm(x) = \\(\\frac{2}{3}\\)x<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nm (x) = \\(\\frac{2}{3}\\)x<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) to plot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table for the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26.jpg\" alt=\"\" width=\"402\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-26-300x66.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-35.png\" alt=\"\" width=\"489\" height=\"459\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-35.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-35-300x282.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 15.<br \/>\nThe function m = 30 &#8211; 3r represents the amount m (in dollars) of money you have after renting r video games. (Section 3.1 and Section 3.2)<br \/>\na. Identify the independent and dependent variables.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nm = 30 &#8211; 3r<br \/>\nWe know that,<br \/>\nThe independent variables are the values of x<br \/>\nThe dependent variables are the values of y<br \/>\nNow,<br \/>\nCompare the given function with<br \/>\ny = mx + c<br \/>\nHence,<br \/>\nThe independent variable of the given function is: r<br \/>\nThe dependent variable of the given function is: m<\/p>\n<p>b. Find the domain and range of the function. Is the domain discrete or continuous? Explain.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nm = 30 &#8211; 3r<br \/>\nNow,<br \/>\nput the values -2, -1, 0, 1, 2 in the place of x and find the values of f(x) to plot a graph [ Remember you can take any value and any number of values]<br \/>\nSo,<br \/>\nThe completed table of the given function is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.jpg\" alt=\"\" width=\"402\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27-300x64.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nWe know that,<br \/>\nThe domain is defined as the set of all the values of x<br \/>\nthe range is defined as the set of all the values of y<br \/>\nHence,<br \/>\nThe domain of the given function is: {-2, -1, 0, 1, 2}<br \/>\nThe range of the given function is: {36, 33, 30, 27, 24, 21}<\/p>\n<p>c. Graph the function using its domain.<br \/>\nAnswer:<br \/>\nThe completed table for the given function from part (b) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.jpg\" alt=\"\" width=\"402\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27.jpg 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-27-300x64.jpg 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nHence,<br \/>\nThe representation of the given function using its domain in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-36.png\" alt=\"\" width=\"479\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-36.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-36-300x291.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 16.<br \/>\nThe function d(x) = 1375 &#8211; 110x represents the distance (in miles) a high-speed train is from its destination after x hours. (Section 3.3)<br \/>\na. How far is the train from its destination after 8 hours?<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nd (x) = 1375 &#8211; 110x<br \/>\nWhere,<br \/>\nd (x) represents the distance (in miles)<br \/>\nx represents the time<br \/>\nNow,<br \/>\nIt is given that we have to find the distance traveled by train after 8 hours i.e., the value of x is given<br \/>\nSo,<br \/>\nd (x) = 1375 &#8211; 110 (8)<br \/>\n= 1375 &#8211; 880<br \/>\n= 495 miles<br \/>\nHence, from the above,<br \/>\nWe can conclude that the distance traveled by train after 8 hours is: 495 miles<\/p>\n<p>b. How long does the train travel before reaching its destination?<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nd (x) = 1375 &#8211; 110x<br \/>\nFrom part (a),<br \/>\nWe find the value of d (x) as: 495 miles<br \/>\nSo,<br \/>\n495 = 1375 &#8211; 110x<br \/>\n110x = 1375 &#8211; 495<br \/>\n110x = 880<br \/>\nx = 880 \/110<br \/>\nx = 8 hours<br \/>\nHence, from the above,<br \/>\nWe can conclude that train travel for 8 hours before reaching its destination<\/p>\n<h3><a id=\"Lesson_3.4_Graphing_Linear_Equations_in_Standard_Form\"><\/a>Lesson 3.4 Graphing Linear Equations in Standard Form<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you describe the graph of the equation Ax + By = C?<br \/>\nAnswer:<br \/>\nWhen A and B are not both zero,<br \/>\nThe graph\u00a0of\u00a0Ax\u00a0+ By =\u00a0C is always a line.<br \/>\nNow,<br \/>\nDivide both sides by B<br \/>\nBecause the form Ax + By = C can describe any line,<br \/>\nIt is called the standard form of an equation for a line.<\/p>\n<p><b>EXPLORATION 1<br \/>\nUsing a Table to Plot Points<br \/>\nWork with a partner. <\/b>You sold a total of $16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are $4 each. Child tickets are $2 each.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-102.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 102.1\" width=\"713\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-102.1.png 713w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-102.1-300x100.png 300w\" sizes=\"(max-width: 713px) 100vw, 713px\" \/><br \/>\na. Let x represent the number of adult tickets. Let y represent the number of child tickets. Use the verbal model to write an equation that relates to x and y.<br \/>\nAnswer:<br \/>\nIt is given that you sold a total of $16 worth of tickets to a fundraiser. You lost track of how many of each type of ticket you sold. Adult tickets are $4 each. Child tickets are $2 each.<br \/>\nIt is also given that<br \/>\nLet x be the number of adult tickets<br \/>\nLet y be the number of child tickets<br \/>\nSo,<br \/>\nThe total cost of tickets = (The cost of the child tickets + The cost of the adult tickets)<br \/>\nThe total cost of tickets = (The number of children) \u00d7 ( The cost of each child ticket ) + ( The numebr of adults ) \u00d7 ( The cost of each adult ticket )<br \/>\nSo,<br \/>\n16 = 2x + 4y<br \/>\n2 (x + 2y) = 16<br \/>\nx + 2y = 16 \/ 2<br \/>\nSo,<br \/>\nx + 2y = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation that relates x and y is:<br \/>\nx + 2y = 8<\/p>\n<p>b. Copy and complete the table to show the different combinations of tickets you might have sold.<br \/>\nAnswer:<br \/>\nThe equation that represents the number of different tickets sold is:<br \/>\nx + 2y = 8<br \/>\n2y = 8 &#8211; x<br \/>\ny = \\(\\frac{8 &#8211; x}{2}\\)<br \/>\nSo,<br \/>\nThe completed table that shows the different combinations of tickets you might have sold is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-28.jpg\" alt=\"\" width=\"239\" height=\"64\" \/><\/p>\n<p>c. Plot the points from the table. Describe the pattern formed by the points.<br \/>\nAnswer:<br \/>\nThe completed table that shows the different combinations of tickets you might have sold is from part (b) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-28.jpg\" alt=\"\" width=\"239\" height=\"64\" \/><br \/>\nThe representation of the ordered pairs from the above table is:<br \/>\n(1, 4), (2, 3), (3, 3), (4, 2), (5, 2)<br \/>\nHence,<br \/>\nThe representation of the points from the table in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-37.png\" alt=\"\" width=\"478\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-37.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-37-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-37-150x150.png 150w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nHence, from the graph,<br \/>\nWe can observe that the pattern drawn by the points is a straight line<\/p>\n<p>d. If you remember how many adult tickets you sold, can you determine how many child tickets you sold? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-104.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 104\" width=\"233\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe given function from part (a) is in the form of<br \/>\ny = mx + c<br \/>\nWhere,<br \/>\ny is the number of adult tickets<br \/>\nx is the number of child tickets<br \/>\nSo,<br \/>\nIf we know the number of adult tickets you sold, i.e., the value of y, then we can find the number of child tickets, i.e., the value of x by putting the value of y in the equation<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that if we know the number of adult tickets you sold, then we can find the number of child tickets you sold<\/p>\n<p><b>EXPLORATION 2<br \/>\nRewriting and Graphing an Equation<br \/>\nWork with a partner.<\/b> You sold a total of $48 worth of cheese. You forgot how many pounds of each type of cheese you sold. Swiss cheese costs $8 per pound. Cheddar cheese costs $6 per pound.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 105\" width=\"387\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105-300x50.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\na. Let x represent the number of pounds of Swiss cheese. Let y represent the number of pounds of cheddar cheese. Use the verbal model to write an equation that relates to x and y.<br \/>\nAnswer:<br \/>\nit is given that you sold a total of $48 worth of cheese. You forgot how many pounds of each type of cheese you sold. Swiss cheese costs $8 per pound. Cheddar cheese costs $6 per pound.<br \/>\nIt is also given that,<br \/>\nx represents the number of pounds of Swiss cheese<br \/>\ny represents the number of pounds of Cheddar cheese<br \/>\nNow,<br \/>\nThe total cost = ( The cost of Swiss Cheese ) + ( The cost of Cheddar Cheese )<br \/>\nThe total cost = ( The number of pounds of Swiss cheese ) \u00d7 ( The cost of Swiss cheese ) + ( The number of pounds of Cheddar cheese ) \u00d7 ( The cost of Cheddar cheese )<br \/>\n48 = 8x + 6y<br \/>\n8x + 6y = 48<br \/>\n2 (4x + 3y) = 48<br \/>\n4x + 3y = 48 \/ 4<br \/>\n4x + 3y = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the equation that relates both x and y is:<br \/>\n4x + 3y = 12<\/p>\n<p>b. Solve the equation for y. Then use a graphing calculator to graph the equation. Given the real-life context of the problem, find the domain and range of the function.<br \/>\nAnswer:<br \/>\nThe equation that relates to x and y from part (a) is:<br \/>\n4x + 3y = 12<br \/>\n3y = 12 &#8211; 4x<br \/>\ny = \\(\\frac{12 &#8211; 4x}{3}\\)<br \/>\nSo,<br \/>\nThe representation of the equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38.png\" alt=\"\" width=\"479\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38-150x150.png 150w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nWe know that,<br \/>\nThe domain is the set of all the values of x in the graph<br \/>\nThe range is the set of all the values of y in the graph<br \/>\nNow,<br \/>\nFrom the graph,<br \/>\nThe domain of the equation is: { -4, -3, -2, -1, 0, 1, 2, 3 }<br \/>\nThe range of the given equation is: {-1, -2, -3, -4, -5, -6, -7, -8, -9, 5, 6, 7, 8, 9, 10}<\/p>\n<p>c. The x-intercept of a graph is the x-coordinate of a point where the graph crosses the x-axis. The y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis. Use the graph to determine the x- and y-intercepts.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{12 &#8211; 4x}{3}\\)<br \/>\nIt is given that the x-intercept of a graph is the x-coordinate of a point where the graph crosses the x-axis. The y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis.<br \/>\nNow,<br \/>\nThe graph from part (b) is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38.png\" alt=\"\" width=\"479\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-38-150x150.png 150w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence,<br \/>\nBy observing the graph,<br \/>\nWe can conclude that<br \/>\nThe x-intercept is: 3<br \/>\nThe y-intercept is: 4<\/p>\n<p>d. How could you use the equation you found in part (a) to determine the x- and y-intercepts? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{12 &#8211; 4x}{3}\\)<br \/>\nWe know that,<br \/>\nWe can obtain the x-intercept by making y term zero<br \/>\nWe can obtain the y-intercept making x term zero<br \/>\nSo,<br \/>\nThe x-intercept is:<br \/>\n0 = \\(\\frac{12 &#8211; 4x}{3}\\)<br \/>\n12 &#8211; 4x = 0<br \/>\n4x = 12<br \/>\nx = 12 \/ 4<br \/>\nx = 3<br \/>\nHence,<br \/>\nThe x-intercept is: 3<br \/>\nThe y-intercept is:<br \/>\ny = \\(\\frac{12 &#8211; 4(0)}{3}\\)<br \/>\ny = 12 \/ 3<br \/>\ny = 4<br \/>\nHence,<br \/>\nThe y-intercept is: 4<\/p>\n<p>e. Explain the meaning of the intercepts in the context of the problem.<br \/>\nAnswer:<br \/>\nAn intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.\u00a0 When the linear function is used to represent a real-world situation, the intercepts\u00a0have significant\u00a0meaning\u00a0in the context of the problem.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you describe the graph of the equation Ax + By = C?<br \/>\nAnswer:<br \/>\nWhen A and B are not both zero,<br \/>\nThe graph\u00a0of\u00a0Ax\u00a0+ By =\u00a0C is always a line.<br \/>\nNow,<br \/>\nDivide both sides by B<br \/>\nBecause the form Ax + By = C can describe any line,<br \/>\nIt is called the standard form of an equation for a line.<\/p>\n<p>Question 4.<br \/>\nWrite a real-life problem that is similar to those shown in Explorations 1 and 2.<br \/>\nAnswer:<br \/>\nThe real-life problem that is similar to those in Explorations\u00a0 1 and 2 is:<br \/>\nThe age of A is twice the age of B and the sum of the twice the age of A and the age of B is 24<\/p>\n<p><b>3.4 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\ny = -2.5<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -2.5<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-39.png\" alt=\"\" width=\"499\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-39.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-39-300x283.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 2.<br \/>\nx = 5<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx = 5<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-40.png\" alt=\"\" width=\"479\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-40.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-40-300x296.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p><b>Use intercepts to graph the linear equation. Label the points corresponding to the intercepts.<\/b><\/p>\n<p>Question 3.<br \/>\n2x &#8211; y = 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n2x &#8211; y = 4<br \/>\nRewrite the given equation in the standard form<br \/>\nWe know that,<br \/>\nThe standard form of the linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = 2x &#8211; 4<br \/>\nTo find the value of x-intercept, put y = 0<br \/>\n2x &#8211; 4 = 0<br \/>\n2x = 4<br \/>\nx = 4 \/ 2<br \/>\nx = 2<br \/>\nTo find the value of y-intercept, put x = 0<br \/>\ny = 2(0) &#8211; 4<br \/>\ny = -4<br \/>\nHence,<br \/>\nThe representation of the given equation corresponding to the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-41.png\" alt=\"\" width=\"483\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-41.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-41-300x293.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><\/p>\n<p>Question 4.<br \/>\nx + 3y = -9<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 3y = -9<br \/>\nRewrite the given equation in the standard form<br \/>\nWe know that,<br \/>\nThe standard form of the linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\n3y = -9 &#8211; x<br \/>\ny = (-9 -x ) \/ 3<br \/>\nNow,<br \/>\nTo find the value of x-intercept, put y = 0<br \/>\n-9 &#8211; x = 0<br \/>\nx = -9<br \/>\nTo find the value of y-intercept, put x = 0<br \/>\ny = (-9 &#8211; 0) \/ 3<br \/>\nt = -9 \/ 3<br \/>\ny = -3<br \/>\nHence,<br \/>\nThe representation of the given equation corresponding to the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-42.png\" alt=\"\" width=\"479\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-42.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-42-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-42-150x150.png 150w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 5.<br \/>\n<b>WHAT IF?<\/b> You decide to rent tables from a different company. The situation can be modeled by the equation 4x + 6y = 180, where x is the number of small tables and y is the number of large tables. Graph the equation and interpret the intercepts.<br \/>\nAnswer:<br \/>\nIt is given that you decide to rent tables from a different company.<br \/>\nThe given equation corresponding to the above situation is given as:<br \/>\n4x + 6y = 180<br \/>\nWhere,<br \/>\nx is the number of small tables<br \/>\ny is the number of large tables<br \/>\nNow,<br \/>\nRewrite the given equation in the standard form of the linear equation<br \/>\nWe know that,<br \/>\nThe standard form of the linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\n6y = 180 &#8211; 4x<br \/>\ny = (180 &#8211; 4x) \/ 6<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\n180 &#8211; 4x = 0<br \/>\n4x = 180<br \/>\nx = 180 \/ 4<br \/>\nx = 45<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\ny = (180 &#8211; 4(0) ) \/ 6<br \/>\ny = 180 \/ 6<br \/>\ny = 30<br \/>\nHence,<br \/>\nThe representation of the given equation corresponding to the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-43.png\" alt=\"\" width=\"479\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-43.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-43-300x294.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Equations_in_Standard_Form_3.4_Exercises\"><\/a>Graphing Linear Equations in Standard Form 3.4 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nHow are x-intercepts and y-intercepts alike? How are they different?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 1\" width=\"592\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-1-300x101.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE did DOESN\u2019T BELONG?<\/b><br \/>\nWhich point does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 105.1\" width=\"435\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105.1.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-105.1-300x37.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\nAnswer:<br \/>\nThe given points are:<br \/>\na. (0, -3)<br \/>\nb. (0, 0)<br \/>\nc. (4, -3)<br \/>\nd. (4, 0)<br \/>\nFrom the above points,<br \/>\nWe can observe that<br \/>\n(0, -3) belongs to the y-axis<br \/>\n(0, 0) belongs to the origin<br \/>\n(4, -3) does not belong either to the x-axis or y-axis<br \/>\n(4, 0) belongs to the x-axis<br \/>\nHence, from the above,<br \/>\nWe can conclude that (4, -3) does not belong with the other three<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20136, graph the linear equation.<\/b><\/p>\n<p>Question 3.<br \/>\nx = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 3\" width=\"204\" height=\"195\" \/><\/p>\n<p>Question 4.<br \/>\ny = 2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 2<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-51.png\" alt=\"\" width=\"476\" height=\"466\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-51.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-51-300x294.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 5.<br \/>\ny = -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 5\" width=\"206\" height=\"193\" \/><\/p>\n<p>Question 6.<br \/>\nx = -1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx = -1<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-52.png\" alt=\"\" width=\"479\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-52.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-52-300x291.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p><b>In Exercises 7\u201312, find the x- and y-intercepts of the graph of the linear equation.<\/b><\/p>\n<p>Question 7.<br \/>\n2x + 3y = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 7\" width=\"424\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-7.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-7-300x164.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 8.<br \/>\n3x + 6y = 24<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x + 6y = 24<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n3x + 0 = 24<br \/>\n3x = 24<br \/>\nx = 24 \/ 3<br \/>\nx = 8<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + 6y = 24<br \/>\n6y = 24<br \/>\ny = 24 \/ 6<br \/>\ny = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe value of the x-intercept is: 8<br \/>\nThe value of the y-intercept is: 4<\/p>\n<p>Question 9.<br \/>\n-4x + 8y = -16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 9\" width=\"447\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-9.png 447w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-9-300x155.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/p>\n<p>Question 10.<br \/>\n-6x + 9y = -18<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-6x + 9y = -18<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n-6x + 0 = -18<br \/>\n-6x = -18<br \/>\n6x = 18<br \/>\nx = 18 \/ 6<br \/>\nx = 3<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + 9y = -18<br \/>\n9y = -18<br \/>\ny = -18 \/ 9<br \/>\ny = -2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe value of the x-intercept is: 3<br \/>\nThe value of the y-intercept is: -2<\/p>\n<p>Question 11.<br \/>\n3x &#8211; 6y = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 11\" width=\"444\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-11.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-11-300x186.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 12.<br \/>\n-x + 8y = 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-x + 8y = 4<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n-x + 0 = 4<br \/>\n-x = 4<br \/>\nx = -4<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + 8y = 4<br \/>\n8y = 4<br \/>\ny = 4 \/ 8<br \/>\ny = 1 \/ 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe value of the x-intercept is: -4<br \/>\nThe value of the y-intercept is: 1\/2<\/p>\n<p><b>In Exercises 13\u201322, use intercepts to graph the linear equation. Label the points corresponding to the intercepts.<\/b><\/p>\n<p>Question 13.<br \/>\n5x + 3y = 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 13\" width=\"406\" height=\"579\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-13.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-13-210x300.png 210w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 14.<br \/>\n4x + 6y = 12<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n4x + 6y = 12<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n4x + 0 = 12<br \/>\n4x = 12<br \/>\nx = 12 \/ 4<br \/>\nx = 3<br \/>\nTo find the y-intercept, put x = 0<br \/>\n0 + 6y = 12<br \/>\n6y = 12<br \/>\ny = 12 \/ 6<br \/>\ny = 2<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-46.png\" alt=\"\" width=\"477\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-46.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-46-300x294.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>Question 15.<br \/>\n-12x + 3y = 24<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 15\" width=\"426\" height=\"535\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-15.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-15-239x300.png 239w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Question 16.<br \/>\n-2x + 6y = 18<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-2x + 6y = 18<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n-2x + 0 = 18<br \/>\n-2x = 18<br \/>\nx = -18 \/ 2<br \/>\nx = -9<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + 6y = 18<br \/>\n6y = 18<br \/>\ny = 18 \/ 6<br \/>\ny = 3<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-47.png\" alt=\"\" width=\"471\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-47.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-47-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-47-150x150.png 150w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Question 17.<br \/>\n-4x + 3y = -30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 17\" width=\"455\" height=\"597\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-17.png 455w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-17-229x300.png 229w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 18.<br \/>\n-2x + 7y = -21<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n-2x + 7y = -21<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\n-2x + 0 = -21<br \/>\n-2x = -21<br \/>\n2x = 21<br \/>\nx = 21\/2<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + 7y = -21<br \/>\n7y = -21<br \/>\ny = -21 \/ 7<br \/>\ny = -3<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-48.png\" alt=\"\" width=\"476\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-48.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-48-300x296.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 19.<br \/>\n-x + 2y = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 19\" width=\"424\" height=\"463\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-19.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-19-275x300.png 275w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 20.<br \/>\n3x &#8211; y = -5<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x &#8211; y = -5<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n3x &#8211; 0 = -5<br \/>\n3x =\u00a0 -5<br \/>\nx = -5\/3<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 &#8211; y = -5<br \/>\n-y = -5<br \/>\ny = 5<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-49.png\" alt=\"\" width=\"487\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-49.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-49-300x283.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 21.<br \/>\n&#8211;\\(\\frac{5}{2}\\)x + y = 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 21.1\" width=\"440\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.1.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.1-300x188.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 21.2\" width=\"270\" height=\"375\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.2.png 270w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-21.2-216x300.png 216w\" sizes=\"(max-width: 270px) 100vw, 270px\" \/><\/p>\n<p>Question 22.<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + y = -4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + y = -4<br \/>\nNow,<br \/>\nTo find the x-intercept, put y =0<br \/>\nSo,<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + 0 = -4<br \/>\n&#8211;\\(\\frac{1}{2}\\)x = -4<br \/>\n-x = -4(2)<br \/>\n-x = -8<br \/>\nx = 8<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n0 + y = -4<br \/>\ny = -4<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-50.png\" alt=\"\" width=\"474\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-50.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-50-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-50-150x150.png 150w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 23.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation 4x + 6y = 48 models this situation, where x is the number of cars and y is the number of vans.<br \/>\na. Graph the equation. Interpret the intercepts.<br \/>\nb. Find four possible solutions in the context of the problem.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 23.1\" width=\"442\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.1.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.1-294x300.png 294w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 23.2\" width=\"851\" height=\"637\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.2.png 851w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.2-300x225.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.2-768x575.png 768w\" sizes=\"(max-width: 851px) 100vw, 851px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 23.3\" width=\"799\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.3.png 799w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.3-300x38.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-23.3-768x97.png 768w\" sizes=\"(max-width: 799px) 100vw, 799px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.<br \/>\na. Graph the equation. Interpret the intercepts.<br \/>\nAnswer:<br \/>\nIt is given that you are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts.<br \/>\nThe above situation is represented by the equation<br \/>\n10x + 12y = 300<br \/>\nwhere,<br \/>\nx is the number of short-sleeved shirts<br \/>\ny is the number of long-sleeved shirts.<br \/>\nNow,<br \/>\nThe given equation is:<br \/>\n10x + 12y = 300<br \/>\nTo find the x-intercept, put y =0<br \/>\nSo,<br \/>\n10x + 12 (0) = 300<br \/>\n10x = 300<br \/>\nx = 300 \/ 10<br \/>\nx = 30<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\n10 (0) + 12y = 300<br \/>\n12y = 300<br \/>\ny = 300 \/ 12<br \/>\ny = 25<br \/>\nHence,<br \/>\nThe representation of the given equation along with the intercepts in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-45.png\" alt=\"\" width=\"481\" height=\"467\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-45.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-45-300x291.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>b. Twelve students decide they want short-sleeved shirts. How many long-sleeved shirts can you order?<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n10x + 12y = 300<br \/>\nwhere,<br \/>\nx is the number of short-sleeved shirts<br \/>\ny is the number of long-sleeved shirts.<br \/>\nIt is given that 12 students decided they want short-sleeved shirts<br \/>\nSo,<br \/>\nThe number of short-sleeved shirts = 12<br \/>\nSo,<br \/>\n10 (12) + 12y = 300<br \/>\n120 + 12y = 300<br \/>\n12y = 300 &#8211; 120<br \/>\n12y = 180<br \/>\ny = 180 \/ 12<br \/>\ny = 15<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of long-sleeved shirts is: 15<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 25 and 26, describe and correct the error in finding the intercepts of the graph of the equation.<\/b><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-106.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 106\" width=\"330\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-106.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-106-300x145.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 25\" width=\"548\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-25.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-25-300x163.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-107.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 107\" width=\"328\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-107.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-107-300x166.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n4x + 10y = 20<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n4x + 10 (0) = 20<br \/>\n4x = 20<br \/>\nx = 20 \/ 4<br \/>\nx = 5<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n4 (0) + 10y = 20<br \/>\n10y = 20<br \/>\ny = 20 \/ 10<br \/>\ny = 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe x-intercept is: (5, 0)<br \/>\nThe y-intercept is: (0, 2)<\/p>\n<p>Question 27.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYou overhear your friend explaining how to find intercepts to a classmate. Your friend says, \u201cWhen you want to find the x-intercept, just substitute 0 for x and continue to solve the equation.\u201d Is your friend\u2019s explanation correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 27\" width=\"582\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-27.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-27-300x46.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nYou lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game. The team misses all the 1-point baskets and still scores 54 points. The equation 2x + 3y = 54 models the total points scored, where x is the number of 2-point baskets made and y is the number of 3-point baskets made.<br \/>\na. Find and interpret the intercepts.<br \/>\nAnswer:<br \/>\nIt is given that you lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game.<br \/>\nIt is also given that the team misses all the 1-point baskets and still scores 54 points.<br \/>\nThe above situation can be described by the equation:<br \/>\n2x + 3y = 54<br \/>\nwhere,<br \/>\nx is the number of 2-point baskets made<br \/>\ny is the number of 3-point baskets made.<br \/>\nSo,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n2x = 54<br \/>\nx = 54 \/ 2<br \/>\nx = 27<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\n3y = 54<br \/>\ny = 54 \/ 3<br \/>\ny = 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe value of the x-intercept is: 27<br \/>\nThe value of the y-intercept is: 18<\/p>\n<p>b. Can the number of 3-point baskets made be odd? Explain your reasoning.<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe number of 3-point baskets can be represented as: y<br \/>\nSo,<br \/>\nTo make the 3-point baskets odd, the multiples of 3 must be odd<br \/>\nBut, in this scenario, it is not possible<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of 3-point baskets made not be odd<\/p>\n<p>c. Graph the equation. Find two more possible solutions in the context of the problem.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-44.png\" alt=\"\" width=\"479\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-44.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-44-300x293.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nThe given equation is:<br \/>\n2x + 3y = 54<br \/>\nFrom the graph,<br \/>\nWe can observe that there are many solutions like (3, 16), (6, 14), (10, 11) and so on<br \/>\nNow,<br \/>\nTo satisfy the above equation, substitute the points we obtained from the graph<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given equation are: (3, 16) and (6, 14)<\/p>\n<p><b>MULTIPLE REPRESENTATIONS<br \/>\nIn Exercises 29\u201332, match the equation with its graph.<br \/>\n<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-108.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 108\" width=\"338\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-108.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-108-300x271.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 29.<br \/>\n5x + 3y = 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 29\" width=\"525\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-29.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-29-300x149.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 30.<br \/>\n5x + 3y = -30<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n5x + 3y = -30<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n5x = -30<br \/>\nx = -30 \/ 5<br \/>\nx = -6<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n3y = -30<br \/>\ny = -30 \/ 3<br \/>\ny = -10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph C) matches the given equation<\/p>\n<p>Question 31.<br \/>\n5x &#8211; 3y = 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 31\" width=\"538\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-31.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-31-300x146.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 32.<br \/>\n5x &#8211; 3y = -30<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n5x &#8211; 3y = -30<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n5x = -30<br \/>\nx = -30 \/ 5<br \/>\nx = -6<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n-3y = -30<br \/>\n3y = 30<br \/>\ny = 30 \/ 3<br \/>\ny = 10<br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph B) matches the given equation<\/p>\n<p>Question 33.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nGraph the equations x = 5, x = 2, y = -2, and y = 1. What enclosed shape do the lines form? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 33\" width=\"562\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-33.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-33-300x164.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> You are organizing a class trip to an amusement park. The cost to enter the park is $30. The cost to enter with a meal plan is $45. You have a budget of $2700 for the trip. The equation 30x + 45y = 2700 models the total cost for the class to go on the trip, where x is the number of students who do not choose the meal plan and y is the number of students who do choose the meal plan.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 109\" width=\"255\" height=\"246\" \/><br \/>\na. Interpret the intercepts of the graph.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 109\" width=\"255\" height=\"246\" \/><br \/>\nWe know that,<br \/>\nThe x-intercept is the point that cuts the x-axis and y must be 0<br \/>\nThe y-intercept is the point that cuts the y-axis and x must be 0<br \/>\nHence,<br \/>\nFrom the graph,<br \/>\nWe can conclude that<br \/>\nThe x-intercept is: (90, 0)<br \/>\nThe y-intercept is: (0, 60)<\/p>\n<p>b. Describe the domain and range in the context of the problem.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-109.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 109\" width=\"255\" height=\"246\" \/><br \/>\nWe know that,<br \/>\nThe domain is defined as the set of all the values of x<br \/>\nThe range is defined as the set of all the values of y<br \/>\nHence,<br \/>\nThe domain of the given function is: {0, 10, 20, 30, 40, 50, 60, 70, 80, 90}<br \/>\nThe range of the given function is: {0, 10, 20, 30, 40, 50, 60}<\/p>\n<p>Question 35.<br \/>\n<b>REASONING<\/b><br \/>\nUse the values to fill in the equation <img loading=\"lazy\" class=\"alignnone size-full wp-image-36385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-110.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 110\" width=\"132\" height=\"26\" \/> so that the x-intercept of the graph is -10 and the y-intercept of the graph is 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-110.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 110.1\" width=\"288\" height=\"46\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 35\" width=\"507\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-35.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-35-300x154.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nWrite an equation in the standard form of a line whose intercepts are integers. Explain how you know the intercepts are integers.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nThe equation in the standard form is:<br \/>\ny = mx + c<br \/>\nNow,<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\nmx = -c<br \/>\nx = &#8211;\\(\\frac{c}{m}\\)<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\ny = 0 + c<br \/>\ny = c<br \/>\nNow, from the above<br \/>\nWe can observe that to make the x and y-intercepts integers, the values of the intercepts must be the multiples of the variable c<\/p>\n<p>Question 37.<br \/>\n<b>WRITING<\/b><br \/>\nAre the equations of horizontal and vertical lines written in standard form? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 37\" width=\"585\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-37.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-37-300x30.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nThe x- and y-intercepts of the graph of the equation 3x + 5y = k are integers. Describe the values of k. Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x + 5y = k<br \/>\nTo find the value of the x-intercept, put y = 0<br \/>\nSo,<br \/>\n3x = k<br \/>\nSo,<br \/>\nThe values of k so that k become integer is 0, 1, 2, and so on<br \/>\nTo find the value of the y-intercept, put x = 0<br \/>\nSo,<br \/>\n5y = k<br \/>\nSo,<br \/>\nThe values of k so that k becomes integer is 0, 1, 2, and so on<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of k so that the x and y-intercepts become integers are: 0, 1, 2, and so on<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-111.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 111\" width=\"78\" height=\"45\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 39\" width=\"275\" height=\"58\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-112.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 112\" width=\"62\" height=\"46\" \/><br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n\\(\\frac{14 -18}{0 &#8211; 2}\\)<br \/>\n= \\(\\frac{-4}{-2}\\)<br \/>\n= \\(\\frac{4}{2}\\)<br \/>\n= 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given expression is: 2<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-113.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 113\" width=\"72\" height=\"43\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.4 Question 41\" width=\"338\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-41.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.4-Question-41-300x51.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-114.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 114\" width=\"92\" height=\"47\" \/><br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n\\(\\frac{12 &#8211; 17}{-5 &#8211; (-2)}\\)<br \/>\n= \\(\\frac{12 &#8211; 17}{-5 + 2}\\)<br \/>\n= \\(\\frac{-5}{-3}\\)<br \/>\n= \\(\\frac{5}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given expression is: \\(\\frac{5}{3}\\)<\/p>\n<h3><a id=\"Lesson_3.5_Graphing_Linear_Equations_in_Slope-Intercept_Form\"><\/a>Lesson 3.5 Graphing Linear Equations in Slope-Intercept Form<\/h3>\n<p><b>EXPLORATION 1<br \/>\nFinding Slopes and y-Intercepts<br \/>\nWork with a partner. <\/b>Find the slope and y-intercept of each line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 115\" width=\"468\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115-300x122.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 115\" width=\"468\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-115-300x122.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\nWe know that,<br \/>\nThe standard form of a linear equation is:<br \/>\ny = mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nNow,<br \/>\na.<br \/>\nThe given equation is:<br \/>\ny = \\(\\frac{2}{3}\\)x + 2<br \/>\nNow,<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\nBy comparison,<br \/>\nWe get,<br \/>\nm = \\(\\frac{2}{3}\\) and c = 2<\/p>\n<p>b.<br \/>\nThe given equation is:<br \/>\ny = -2x &#8211; 1<br \/>\nNow,<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\nBy comparison,<br \/>\nWe get,<br \/>\nm = -2 and c = -1<\/p>\n<p><b>EXPLORATION 2<br \/>\nWriting a Conjecture<br \/>\nWork with a partner.<\/b> Graph each equation. Then copy and complete the table. Use the completed table to write a conjecture about the relationship between the graph of y = mx + b and the values of m and b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-116.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 116\" width=\"226\" height=\"197\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 117\" width=\"520\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117-300x92.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 117\" width=\"520\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-117-300x92.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\nNow,<br \/>\nThe representation of the given equations in the coordinate plane is as follows:<br \/>\nNow,<br \/>\na.<br \/>\nThe given equation is:<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + 3<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-53.png\" alt=\"\" width=\"479\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-53.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-53-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-53-150x150.png 150w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nb.<br \/>\nThe given equation is:<br \/>\ny = 2x &#8211; 2<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-54.png\" alt=\"\" width=\"473\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-54.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-54-300x297.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nc.<br \/>\nThe given equation is:<br \/>\ny = -x + 1<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-55.png\" alt=\"\" width=\"474\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-55.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-55-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-55-150x150.png 150w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\nd.<br \/>\nThe given equation is:<br \/>\ny = x &#8211; 4<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-56.png\" alt=\"\" width=\"479\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-56.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-56-300x294.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe standard form of a linear equation is:<br \/>\ny = mx + b<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nb is the y-intercept<br \/>\nHence,<br \/>\nThe completed table for the above equations&#8217; slopes and y-intercepts is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-60923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29.jpg\" alt=\"\" width=\"520\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29.jpg 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-29-300x93.jpg 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you describe the graph of the equation y = mx + b?<br \/>\na. How does the value of m affect the graph of the equation?<br \/>\nb. How does the value of b affect the graph of the equation?<br \/>\nc. Check your answers to parts (a) and (b) by choosing one equation from Exploration 2 and (1) varying only m and (2) varying only b.<br \/>\nAnswer:<br \/>\nThe graph of the equation<br \/>\ny = mx + b<br \/>\nis a straight line<br \/>\nNow,<br \/>\na.<br \/>\nThe value of m affects the steepness of the line. It also describes the direction (positive or negative). The value of m defines the constant rate of change of variables<\/p>\n<p>b.<br \/>\nThe value of b affects the line to where it should have the point of intersection with the y-axis<\/p>\n<p>c.<br \/>\nThe examples of how m and b varies are as follows:<br \/>\ny =-3x &#8211; 3<br \/>\ny = 2x + 8<br \/>\ny = -3x + 6<br \/>\nHence,<br \/>\nThe slopes and y-intercepts of the above equations are:<br \/>\nm = -3 and b = -3<br \/>\nm = 2 and b = 8<br \/>\nm = -3 and b = 6<\/p>\n<p><b>3.5 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Describe the slope of the line. Then find the slope.<\/b><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-118.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 118\" width=\"150\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-118.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 118\" width=\"150\" height=\"154\" \/><br \/>\nFrom the graph,<br \/>\nThe given points are:<br \/>\n(-4, 3), (1, 1)<br \/>\nWe know that,<br \/>\nThe slope of the line when the two points are given is:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe points are represented as (x, y)<br \/>\nSo,<br \/>\nThe first point is represented as (x1, y1)<br \/>\nThe second point is represented as (x2, y2)<br \/>\nSo,<br \/>\n(x1, y1) = (-4, 3) and (x2, y2) = (1, 1)<br \/>\nHence,<br \/>\nm = \\(\\frac{1 &#8211; 3}{1 &#8211; [-4]}\\)<br \/>\nm = \\(\\frac{-2}{1 + 4}\\)<br \/>\nm = \\(\\frac{-2}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given graph is: \\(\\frac{-2}{5}\\)<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-119.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 119\" width=\"150\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-119.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 119\" width=\"150\" height=\"155\" \/><br \/>\nFrom the graph,<br \/>\nThe given points are:<br \/>\n(3, 3), (-3, 1)<br \/>\nWe know that,<br \/>\nThe slope of the line when the two points are given is:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe points are represented as (x, y)<br \/>\nSo,<br \/>\nThe first point is represented as (x1, y1)<br \/>\nThe second point is represented as (x2, y2)<br \/>\nSo,<br \/>\n(x1, y1) = (3, 3) and (x2, y2) = (-3, 1)<br \/>\nHence,<br \/>\nm = \\(\\frac{1 &#8211; 3}{-3 &#8211; 3}\\)<br \/>\nm = \\(\\frac{-2}{6}\\)<br \/>\nm = \\(\\frac{-1}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given graph is: \\(\\frac{-1}{3}\\)<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 120\" width=\"158\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120.png 158w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120-150x150.png 150w\" sizes=\"(max-width: 158px) 100vw, 158px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 120\" width=\"158\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120.png 158w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-120-150x150.png 150w\" sizes=\"(max-width: 158px) 100vw, 158px\" \/><br \/>\nFrom the graph,<br \/>\nThe given points are:<br \/>\n(5, 4), (2, -3)<br \/>\nWe know that,<br \/>\nThe slope of the line when the two points are given is:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nThe points are represented as (x, y)<br \/>\nSo,<br \/>\nThe first point is represented as (x1, y1)<br \/>\nThe second point is represented as (x2, y2)<br \/>\nSo,<br \/>\n(x1, y1) = (5, 4) and (x2, y2) = (2, -3)<br \/>\nHence,<br \/>\nm = \\(\\frac{-3 &#8211; 4}{2 &#8211; 5}\\)<br \/>\nm = \\(\\frac{-7}{-3}\\)<br \/>\nm = \\(\\frac{7}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given graph is: \\(\\frac{7}{3}\\)<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>The points represented by the table lie on a line. How can you find the slope of the line from the table? What is the slope of the line?<\/b><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-121.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 121\" width=\"197\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-121.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 121\" width=\"197\" height=\"68\" \/><br \/>\nFrom the above table,<br \/>\nThe representations of the values of x and y in the form of ordered pairs are:<br \/>\n(2, 10), (4, 15), (6, 20), (8, 25)<br \/>\nNow,<br \/>\nTo find the slope of a line,<br \/>\nTake any 2 ordered pairs and find the slope<br \/>\nNow,<br \/>\nLet,<br \/>\n(x1, y1) = (2, 10) and (x2, y2) = (4, 15)<br \/>\nWe know that,<br \/>\nThe slope of the line when the two points are given is:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nHence,<br \/>\nm = \\(\\frac{15 &#8211; 10}{4 &#8211; 2}\\)<br \/>\nm = \\(\\frac{5}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given graph is: \\(\\frac{5}{2}\\)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-122.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 122\" width=\"196\" height=\"63\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-122.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 122\" width=\"196\" height=\"63\" \/><br \/>\nFrom the above table,<br \/>\nThe representations of the values of x and y in the form of ordered pairs are:<br \/>\n(5, -12), (5, -9), (5, -6), (5, -3)<br \/>\nNow,<br \/>\nTo find the slope of a line,<br \/>\nTake any 2 ordered pairs and find the slope<br \/>\nNow,<br \/>\nLet,<br \/>\n(x1, y1) = (5, -12) and (x2, y2) = (5, -9)<br \/>\nWe know that,<br \/>\nThe slope of the line when the two points are given is:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nHence,<br \/>\nm = \\(\\frac{-9 &#8211; [-12]}{5 &#8211; 5}\\)<br \/>\nm = \\(\\frac{3}{0}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given graph is: undefined<\/p>\n<p><b>Find the slope and the y-intercept of the graph of the linear equation.<\/b><\/p>\n<p>Question 6.<br \/>\ny = -6x + 1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -6x + 1<br \/>\nWe know that,<br \/>\nThe standard representation of a linear equation is:<br \/>\ny\u00a0 mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nNow,<br \/>\nCompare the given equation with the standard representation of the linear equation<br \/>\nHence,<br \/>\nThe values of m and c are: -6 and 1<\/p>\n<p>Question 7.<br \/>\ny = 8<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 8<br \/>\nRewrite the given equation as:<br \/>\ny = 0x + 8<br \/>\nWe know that,<br \/>\nThe standard representation of a linear equation is:<br \/>\ny\u00a0 mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nNow,<br \/>\nCompare the given equation with the standard representation of the linear equation<br \/>\nHence,<br \/>\nThe values of m and c are: 0 and 8<\/p>\n<p>Question 8.<br \/>\nx + 4y = -10<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 4y = -10<br \/>\nRewrite the given equation as:<br \/>\n4y = -10 &#8211; x<br \/>\ny = \\(\\frac{-10 &#8211; x}{4}\\)<br \/>\ny = \\(\\frac{-x}{4}\\) &#8211; \\(\\frac{10}{4}\\)<br \/>\nWe know that,<br \/>\nThe standard representation of a linear equation is:<br \/>\ny\u00a0 mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nNow,<br \/>\nCompare the given equation with the standard representation of the linear equation<br \/>\nHence,<br \/>\nThe values of m and &#8216;c&#8217; are: &#8211;\\(\\frac{1}{4}\\) and &#8211;\\(\\frac{10}{4}\\)<\/p>\n<p><b>Graph the linear equation. Identify the x-intercept.<\/b><\/p>\n<p>Question 9.<br \/>\ny = 4x &#8211; 4<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 4x &#8211; 4<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = 4x &#8211; 4<br \/>\n4x = 4<br \/>\nx = 4 \/ 4<br \/>\nx = 1<br \/>\nHence,<br \/>\nThe representation of the given equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-61195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-57.png\" alt=\"\" width=\"480\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-57.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-57-300x294.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Question 10.<br \/>\n3x + y = -3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n3x + y = -3<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n3x + 0 = -3<br \/>\n3x = -3<br \/>\nx = -3 \/ 3<br \/>\nx = -1<br \/>\nHence,<br \/>\nThe representation of the given equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-61201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-58.png\" alt=\"\" width=\"484\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-58.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-58-300x291.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 11.<br \/>\nx + 2y = 6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + 2y = 6<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\nx + 0 = 6<br \/>\nx = 6<br \/>\nHence,<br \/>\nThe representation of the given equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-61204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-59.png\" alt=\"\" width=\"476\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-59.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-59-300x296.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 12.<br \/>\nA linear function h models a relationship in which the dependent variable decreases 2 units for every 5 units the independent variable increases. Graph h when h(0) = 4. Identify the slope, y-intercept, and x-intercept of the graph.<br \/>\nAnswer:<br \/>\nIt is given that a linear function h models a relationship in which the dependent variable decreases 2 units for every 5 units the independent variable increases.<br \/>\nWe know that,<br \/>\nThe independent variable is: x<br \/>\nthe dependent variable is: y<br \/>\nSo,<br \/>\nSo,<br \/>\nx = -2 and y = +5<br \/>\nSo,<br \/>\nWe can say that the slope is represented as:<br \/>\nm = \\(\\frac{-2}{5}\\)<br \/>\nIt is also given that<br \/>\nh (0) = 2<br \/>\nSo,<br \/>\ny = 2 at x = 0<br \/>\nHence,<br \/>\nThe y-intercept is: (0, 2)<br \/>\nHence,<br \/>\nThe representation of the equation in the standard form is:<br \/>\ny = mx + c<br \/>\ny = &#8211;\\(\\frac{2}{5}\\)x + 2<br \/>\nNow,<br \/>\nThe value of the x-intercept can be obtained by putting y = 0<br \/>\nSo,<br \/>\n0 = &#8211;\\(\\frac{2}{5}\\)x + 2<br \/>\n&#8211;\\(\\frac{2}{5}\\)x = -2<br \/>\n\\(\\frac{2}{5}\\)x = 2<br \/>\nx = \\(\\frac{5 \u00d7 2}{2}\\)<br \/>\nx = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope is: &#8211;\\(\\frac{2}{5}\\)<br \/>\nThe x-intercept is: (5, 0)<br \/>\nThe y-intercept is: (0, 2)<\/p>\n<p>Question 13.<br \/>\n<b>WHAT IF?<\/b> The elevation of the submersible is modeled by h(t) = 500t &#8211; 10,000.<br \/>\n(a) Graph the function and identify its domain and range.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nh(t) = 500t &#8211; 10,000<br \/>\nSo,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-61212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-60.png\" alt=\"\" width=\"477\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-60.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-60-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-60-150x150.png 150w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\nFrom the above graph,<br \/>\nWe can say that the given equation is parallel to the y-axis<br \/>\nHence,<br \/>\nThere are no values for the domain since there are no values of x<br \/>\nThe range of the given function is: -20,000 \u2264 t \u2264 20,000<\/p>\n<p>(b) Interpret the slope and the intercepts of the graph.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nh (t) = 500t &#8211; 10,000<br \/>\nCompare the given equation with the standard linear equation y = mx + c<br \/>\nSo,<br \/>\nm = 500<br \/>\nc = -10,000<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0 or h (t) = 0<br \/>\nSo,<br \/>\n500t &#8211; 10,000 = 0<br \/>\n500t = 10,000<br \/>\nt = 10,000 \/ 500<br \/>\nt = 20 or x = 20<br \/>\nTo find the y-intercept, put x = 0 or t = 0<br \/>\nSo,<br \/>\nh (t) = 500 (0) &#8211; 10,000<br \/>\nh (t) = -10,000<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope is: 500<br \/>\nThe x-intercept is: 20<br \/>\nThe y-intercept is: -10,000<\/p>\n<h3><a id=\"Graphing_Linear_Equations_in_Slope-Intercept_Form_3.5_Exercises\"><\/a>Graphing Linear Equations in Slope-Intercept Form 3.5 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b><br \/>\nThe ________ of a nonvertical line passing through two points is the ratio of the rise to the run.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 1\" width=\"560\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-1-300x31.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b><br \/>\nWhat is a constant function? What is the slope of a constant function?<br \/>\nAnswer:<br \/>\nA &#8220;Constant function&#8221; is a function where the output (y) is the same for every input (x) value.<br \/>\nThe slope for a constant function will be 0<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b><br \/>\nWhat is the slope-intercept form of a linear equation? Explain why this form is called the slope-intercept form.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 3\" width=\"570\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-3.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-3-300x47.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WHICH ONE did DOESN\u2019T BELONG?<\/b> Which equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-122.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 122.1\" width=\"489\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-122.1.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-122.1-300x31.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\na. y = -5x &#8211; 1<br \/>\nb. 2x &#8211; y = 8<br \/>\nc. y = x + 4<br \/>\nd. y = -3x + 13<br \/>\nNow,<br \/>\nRewrite all the above equations in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nNow,<br \/>\na.<br \/>\nThe given equation is:<br \/>\ny = -5x &#8211; 1<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nWe will get,<br \/>\nm = -5 and c = -1<\/p>\n<p>b.<br \/>\nThe given equation is:<br \/>\n2x &#8211; y = 8<br \/>\ny = 2x &#8211; 8<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nWe will get<br \/>\nm = 8 and c = -8<\/p>\n<p>c.<br \/>\nThe given equation is:<br \/>\ny = x + 4<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nWe will get<br \/>\nm = 1 and c = 4<\/p>\n<p>d.<br \/>\nThe given equation is:<br \/>\ny = -3x + 13<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nWe will get<br \/>\nm = -3 and c = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that equation (b) does not belong with the other three since the slope of equation (b) is even whereas all the other slops are odd<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u20138, describe the slope of the line. Then find the slope.<\/b><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-123.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 123\" width=\"135\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 5\" width=\"563\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-5.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-5-300x109.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-124.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 124\" width=\"135\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-124.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 124\" width=\"135\" height=\"130\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the slope falls from right to left<br \/>\nSo,<br \/>\nThe slope is positive<br \/>\nNow,<br \/>\nWe have to represent the first pair as (x1, y1) and the second pair as (x2, y2)<br \/>\nNow,<br \/>\nThe representation of the values of x and y in the form of ordered pairs to find a slope is:<br \/>\n(4, 3), (1, -1)<br \/>\nWe know that,<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{-1 &#8211; 3}{1 &#8211; 4}\\)<br \/>\nm = \\(\\frac{-4}{-3}\\)<br \/>\nm = \\(\\frac{4}{3}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the line is: \\(\\frac{4}{3}\\)<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-125.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 125\" width=\"136\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 7\" width=\"448\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-7.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-7-300x117.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-126.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 126\" width=\"140\" height=\"131\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-126.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 126\" width=\"140\" height=\"131\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the slope falls from left to right<br \/>\nSo,<br \/>\nThe slope is negative<br \/>\nNow,<br \/>\nWe have to represent the first pair as (x1, y1) and the second pair as (x2, y2)<br \/>\nNow,<br \/>\nThe representation of the values of x and y in the form of ordered pairs to find a slope is:<br \/>\n(0, 3), (5, -1)<br \/>\nWe know that,<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{-1 &#8211; 3}{5 &#8211; 0}\\)<br \/>\nm = \\(\\frac{-4}{5}\\)<br \/>\nm = &#8211;\\(\\frac{4}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the line is: &#8211;\\(\\frac{4}{5}\\)<\/p>\n<p><b>In Exercises 9\u201312, the points represented by the table lie on a line. Find the slope of the line.<\/b><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-127.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 127\" width=\"202\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 9\" width=\"459\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-9.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-9-300x78.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-128.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 128\" width=\"199\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-128.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 128\" width=\"199\" height=\"68\" \/><br \/>\nWe know that,<br \/>\nTo find the slope from a given table, we can take any x and y pair from the table<br \/>\nWe have to represent the first pair as (x1, y1) and the second pair as (x2, y2)<br \/>\nNow,<br \/>\nThe representation of the values of x and y in the form of ordered pairs to find a slope is:<br \/>\n(-1, -6), (2, -6)<br \/>\nWe know that,<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{-6 + 6}{2 + 1}\\)<br \/>\nm = \\(\\frac{0}{3}\\)<br \/>\nm = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the line is: 0<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-129.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 129\" width=\"195\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 11\" width=\"260\" height=\"98\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-130.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 130\" width=\"192\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-130.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 130\" width=\"192\" height=\"69\" \/><br \/>\nWe know that,<br \/>\nTo find the slope from a given table, we can take any x and y pair from the table<br \/>\nWe have to represent the first pair as (x1, y1) and the second pair as (x2, y2)<br \/>\nNow,<br \/>\nThe representation of the values of x and y in the form of ordered pairs to find a slope is:<br \/>\n(-4, 2), (-3, -5)<br \/>\nWe know that,<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{-5 &#8211; 2}{-3 &#8211; [-4]}\\)<br \/>\nm = \\(\\frac{-7}{1}\\)<br \/>\nm = -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the line is: -7<\/p>\n<p>Question 13.<br \/>\n<b>ANALYZING A GRAPH<\/b><br \/>\nThe graph shows the distance y(in miles) that a bus travels in x hours. Find and interpret the slope of the line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-131.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 131\" width=\"185\" height=\"190\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 13\" width=\"569\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-13.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-13-300x82.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 14.<br \/>\n<b>ANALYZING A TABLE<\/b><br \/>\nThe table shows the amount x(in hours) of time you spend at a theme park and the admission fee y (in dollars) to the park. The points represented by the table lie on a line. Find and interpret the slope of the line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-132.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 132\" width=\"196\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-132.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 132\" width=\"196\" height=\"132\" \/><br \/>\nIt is given that the table shows the amount x(in hours) of time you spend at a theme park and the admission fee y (in dollars) to the park and the points represented by the table lie on a line.<br \/>\nNow,<br \/>\nThe representations of the x and y values in the form of ordered pairs i.e., (x, y)<br \/>\nSo,<br \/>\nLet (6, 54.99) and (7, 54.99) be the 2 ordered pairs<br \/>\nWe know that,<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nm = \\(\\frac{54.99 &#8211; 54.99}{7 &#8211; 6}\\)<br \/>\nm = \\(\\frac{0}{1}\\)<br \/>\nm = 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the line is: 0<\/p>\n<p><b>In Exercises 15\u201322, find the slope and the y-intercept of the graph of the linear equation.<\/b><\/p>\n<p>Question 15.<br \/>\ny = -3x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 15\" width=\"380\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-15.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-15-300x83.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 16.<br \/>\ny = 4x &#8211; 7<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 4x &#8211; 7<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nBy comparing, we will get<br \/>\nm = 4 and c = -7<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation (m) is: 4<br \/>\nThe y-intercept of the given equation is: -7<\/p>\n<p>Question 17.<br \/>\ny = 6x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 17\" width=\"357\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-17.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-17-300x83.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Question 18.<br \/>\ny = -1<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -1<br \/>\nRewrite the given equation in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = 0x &#8211; 1<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nBy comparing, we will get<br \/>\nm = 0 and c = -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation (m) is: 0<br \/>\nThe y-intercept of the given equation is: -1<\/p>\n<p>Question 19.<br \/>\n-2x + y = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 19\" width=\"354\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-19.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-19-300x116.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 20.<br \/>\nx + y = -6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx + y = -6<br \/>\nRewrite the given equation in the form of the linear equation<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = -x &#8211; 6<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nBy comparing, we will get<br \/>\nm = -1 and c = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation (m) is: -1<br \/>\nThe y-intercept of the given equation is: -6<\/p>\n<p>Question 21.<br \/>\n-5x = 8 &#8211; y<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 21\" width=\"360\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-21.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-21-300x172.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><\/p>\n<p>Question 22.<br \/>\n0 = 1 &#8211; 2y + 14x<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n0 =1 &#8211; 2y + 14x<br \/>\nRewrite the give equation in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\n2y = 14x + 1<br \/>\nDivide by 2 into both sides<br \/>\ny = (14 \/ 2)x + (1 \/ 2)<br \/>\ny = 7x + \\(\\frac{1}{2}\\)<br \/>\nCompare the given equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nBy comparing, we will get<br \/>\nm = 7 and c = \\(\\frac{1}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation (m) is: 7<br \/>\nThe y-intercept of the given equation is:\\(\\frac{1}{2}\\)<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 23 and 24, describe and correct the error in finding the slope and the y-intercept of the graph of the equation.<\/b><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-133.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 133\" width=\"241\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 23\" width=\"554\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-23.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-23-300x212.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-134.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 134\" width=\"241\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 3x &#8211; 6<br \/>\nCompare the above equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nWe will get<br \/>\nm = 3 and c = -6<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation (m) is: 3<br \/>\nThe y-intercept of the given equation is: -6<\/p>\n<p><b>In Exercises 25\u201332, graph the linear equation. Identify the x-intercept.<\/b><\/p>\n<p>Question 25.<br \/>\ny = -x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 25\" width=\"460\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-25.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-25-300x232.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Question 26.<br \/>\ny = \\(\\frac{1}{2}\\)x + 3<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\ny = \\(\\frac{1}{2}\\)x + 3<br \/>\nTo find the x-intercepy, put y = 0<br \/>\n0 = \\(\\frac{1}{2}\\)x + 3<br \/>\n&#8211;\\(\\frac{1}{2}\\)x = 3<br \/>\nx = 3 (-2)<br \/>\nx = -6<br \/>\nHence,<br \/>\nThe representation of the given linear equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-70.png\" alt=\"\" width=\"479\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-70.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-70-300x293.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 27.<br \/>\ny = 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 27\" width=\"365\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-27.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-27-300x258.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<p>Question 28.<br \/>\ny = -x<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\ny = -x<br \/>\nRewrite the given equation in the form of y = mx + c<br \/>\nSo,<br \/>\ny = -x + 0<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = -x + 0<br \/>\nx = 0<br \/>\nHence,<br \/>\nThe representation of the given linear equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-71.png\" alt=\"\" width=\"486\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-71.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-71-300x290.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 29.<br \/>\n3x + y = -1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 29\" width=\"564\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-29.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-29-300x206.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 30.<br \/>\nx + 4y = 8<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\nx + 4y = 8<br \/>\n4y = -x + 8<br \/>\nDivide by 4 into both sides<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + (8 \/ 4)<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + 2<br \/>\nTo find the x-intercept, put y = 0<br \/>\n0 = &#8211;\\(\\frac{1}{4}\\)x + 2<br \/>\n\\(\\frac{1}{4}\\)x = 2<br \/>\nx = 2(4)<br \/>\nx = 8<br \/>\nHence,<br \/>\nThe representation of the given linear equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-72.png\" alt=\"\" width=\"481\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-72.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-72-300x294.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 31.<br \/>\n-y + 5x = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 31\" width=\"433\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-31.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-31-275x300.png 275w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Question 32.<br \/>\n2x &#8211; y + 6 = 0<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\n2x &#8211; y + 6 = 0<br \/>\nSo,<br \/>\ny = 2x + 6<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = 2x + 6<br \/>\n-2x = 6<br \/>\nx = -6 \/ 2<br \/>\nx = -3<br \/>\nHence,<br \/>\nThe representation of the given linear equation along with the x-intercept in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-73.png\" alt=\"\" width=\"477\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-73.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-73-300x296.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p><b>In Exercises 33 and 34, graph the function with the given description. Identify the slope, y-intercept, and x-intercept of the graph.<\/b><\/p>\n<p>Question 33.<br \/>\nA linear function f models a relationship in which the dependent variable decreases 4 units for every 2 units the independent variable increases. The value of the function at 0 is -2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 33\" width=\"470\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-33.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-33-300x248.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 34.<br \/>\nA linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.<br \/>\nAnswer:<br \/>\nIt is given that a linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases.<br \/>\nWe know that,<br \/>\nThe independent variable is: x<br \/>\nThe dependent variable is: y<br \/>\nSo,<br \/>\nSlope (m) = y \/ x<br \/>\nm = 1 \/ (-5)<br \/>\nm = &#8211;\\(\\frac{1}{5}\\)<br \/>\nIt is given that the value of the function at 0 is 3<br \/>\nSo,<br \/>\nThe value of y at x = 0 is: 3<br \/>\nHence,<br \/>\nThe y-intercept of the given function is: 3<br \/>\nHence,<br \/>\nThe representation of the slope and the y-intercept in the standard form of the linear function s:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\ny = &#8211;\\(\\frac{1}{5}\\)x + 3<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = &#8211;\\(\\frac{1}{5}\\)x + 3<br \/>\n\\(\\frac{1}{5}\\)x = 3<br \/>\nx = 3(5)<br \/>\nx = 15<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\ny = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given function is: &#8211;\\(\\frac{1}{5}\\)<br \/>\nThe x-intercept is: 15<br \/>\nThe y-intercept is: 3<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-69.png\" alt=\"\" width=\"474\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-69.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-69-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-69-150x150.png 150w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 35.<br \/>\n<b>GRAPHING FROM A VERBAL DESCRIPTION<\/b><br \/>\nA linear function r models the growth of your right index fingernail. The length of the fingernail increases 0.7 millimeters every week. Graph r when r(0) = 12. Identify the slope and interpret the y-intercept of the graph.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 35\" width=\"576\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-35.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-35-300x276.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>GRAPHING FROM A VERBAL DESCRIPTION<\/b><br \/>\nA linear function m models the amount of milk sold by a farm per month. The amount decreases 500 gallons for every $1 increase in price. Graph m when m(0) = 3000. Identify the slope and interpret the x- and y-intercepts of the graph.<br \/>\nAnswer:<br \/>\nIt is given that the amount of milk decreases 500 gallons for every $1 increase<br \/>\nFrom the above,<br \/>\nWe can say that,<br \/>\nThe price is the independent variable<br \/>\nSo,<br \/>\nx represents the price<br \/>\nThe amount of milk is the dependent variable<br \/>\nSo,<br \/>\ny represents the amount of milk<br \/>\nSo,<br \/>\nSlope = y \/ x<br \/>\nSlope = -500 \/ 1<br \/>\nSo,<br \/>\nSlope (m) = -500<br \/>\nIt is given that,<br \/>\nm (0) = 3000<br \/>\nWe know that,<br \/>\nm (0) is the functional representation of y<br \/>\nSo,<br \/>\ny = 3000 when x = 0<br \/>\nHence,<br \/>\nThe y-intercept is: 3000<br \/>\nNow,<br \/>\nThe representation of the slope and the y-intercept in the standard form of the linear equation is:<br \/>\ny = ,x + c<br \/>\ny = -500x + 3000<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = -500x + 3000<br \/>\n500x = 3000<br \/>\nx = 3000 \/ 500<br \/>\nx = 6<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\ny = -500 (0) + 3000<br \/>\ny = 3000<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation is: -500<br \/>\nThe c-intercept or y-intercept of the given equation is: 3000<br \/>\nThe x-intercept of the given equation is: 6<\/p>\n<p>Question 37.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-135.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 135\" width=\"252\" height=\"166\" \/><br \/>\na. Graph the function and identify its domain and range.<br \/>\nb. Interpret the slope and the d-intercept of the graph.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 37\" width=\"537\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-37.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-37-300x268.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function c(x) = 0.5x + 70 represents the cost c (in dollars) of renting a truck from a moving company, where x is the number of miles you drive the truck.<br \/>\na. Graph the function and identify its domain and range.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nc (x) = 0.5x + 70<br \/>\nWhere,<br \/>\nrepresents the cost c (in dollars) of renting a truck from a moving company,<br \/>\nx is the number of miles you drive the truck.<br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-68.png\" alt=\"\" width=\"479\" height=\"468\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-68.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-68-300x293.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nWe know that,<br \/>\nThe domain is the set of all the values of x that holds the given equation true<br \/>\nThe range is defined as the set of all the values of y that holds the given equation true<br \/>\nHence,<br \/>\nThe domain of the given function is: -100 \u2264 x \u2264 60<br \/>\nThe range of the given function is: 20 \u2264y \u2264 70<\/p>\n<p>b. Interpret the slope and the c-intercept of the graph.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nc (x) = 0.5x + 70<br \/>\nCompare the above equation with the standard form of the linear function<br \/>\ny = mx + c<br \/>\nSO,<br \/>\nBy comparing, we get<br \/>\nm = 0.5 and c = 70<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given function is: 0.5<br \/>\nThe c-intercept is: 70<\/p>\n<p>Question 39.<br \/>\n<b>COMPARING FUNCTIONS<\/b><br \/>\nA linear function models the cost of renting a truck from a moving company. The table shows the cost y (in dollars) when you drive the truck x miles. Graph the function and compare the slope and the y-intercept of the graph with the slope and the c-intercept of the graph in Exercise 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-136.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 136\" width=\"198\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 39\" width=\"549\" height=\"610\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-39.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-39-270x300.png 270w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 40 and 41, describe and correct the error in graphing the function.<\/b><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-137.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 137\" width=\"296\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny + 1 = 3x<br \/>\nRewrite the above equation in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nThe given equation can be rewritten as:<br \/>\ny = 3x &#8211; 1<br \/>\nNow,<br \/>\nCompare the above equation with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nBy comparison,<br \/>\nWe get<br \/>\nm = 3 and c = -1<br \/>\nHence,<br \/>\nThe representation of the given equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-67.png\" alt=\"\" width=\"481\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-67.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-67-300x296.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-138.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 138\" width=\"310\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-138.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-138-300x173.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 41\" width=\"581\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-41.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-41-300x155.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nGraph the four equations in the same coordinate plane.<br \/>\n3y = -x &#8211; 3<br \/>\n2y &#8211; 14 = 4x<br \/>\n4x &#8211; 3 &#8211; y = 0<br \/>\nx &#8211; 12 = -3y<br \/>\na. What enclosed shape do you think the lines form? Explain.<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\na. 3y = -x &#8211; 3<br \/>\nb. 2y &#8211; 14 = 4x<br \/>\nc. 4x &#8211; 3 &#8211; y = 0<br \/>\nd. x &#8211; 12 = -3y<br \/>\nNow,<br \/>\nRewrite the given equations in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\na.<br \/>\nThe given equation is:<br \/>\n3y = -x &#8211; 3<br \/>\nDivide by 3 into both sides<br \/>\ny = &#8211;\\(\\frac{x}{3}\\) &#8211; (3 \/ 3)<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 1<\/p>\n<p>b.<br \/>\nThe given equation is:<br \/>\n2y &#8211; 14 = 4x<br \/>\nDivide by 2 into both sides<br \/>\ny &#8211; (14 \/ 2) = 2x<br \/>\ny &#8211; 7 = 2x<br \/>\ny = 2x + 7<\/p>\n<p>c.<br \/>\nThe given equation is:<br \/>\n4x &#8211; 3 &#8211; y = 0<br \/>\ny = 4x &#8211; 3<\/p>\n<p>d.<br \/>\nThe given equation is:<br \/>\nx &#8211; 12 = -3y<br \/>\nDivide by -3 into both sides<br \/>\ny = &#8211;\\(\\frac{x}[3]\\) + (12 \/ 3)<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + 4<br \/>\nHence,<br \/>\nThe representations of the given four equations in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-66.png\" alt=\"\" width=\"617\" height=\"513\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-66.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-66-300x249.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><br \/>\nHence,<br \/>\nBy observing the graph,<br \/>\nWe can conclude that the enclosed lines in the graph form a rectangle<\/p>\n<p>b. Write a conjecture about the equations of parallel lines.<br \/>\nAnswer:<br \/>\nWe can\u00a0determine\u00a0from their\u00a0equations whether two lines are parallel\u00a0by comparing their slopes.<br \/>\nIf\u00a0the slopes are the same and the y-intercepts are different, the\u00a0lines are parallel.<br \/>\nIf\u00a0the slopes are different, the\u00a0lines\u00a0are not\u00a0parallel.<br \/>\nUnlike\u00a0parallel lines, perpendicular\u00a0lines\u00a0do intersect.<\/p>\n<p>Question 43.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> The graph shows the relationship between the width y and the length x of a rectangle in inches. The perimeter of a second rectangle is 10 inches less than the perimeter of the first rectangle.<br \/>\na. Graph the relationship between the width and length of the second rectangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-139.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 139\" width=\"164\" height=\"170\" \/><br \/>\nb. How does the graph in part (a) compare to the graph shown?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 43.1\" width=\"584\" height=\"512\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.1-300x263.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 43.2\" width=\"584\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.2.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-43.2-300x180.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nThe graph shows the relationship between the base length x and the side length (of the two equal sides) y of an isosceles triangle in meters. The perimeter of a second isosceles triangle is 8 meters more than the perimeter of the first triangle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-140.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 140\" width=\"179\" height=\"119\" \/><br \/>\na. Graph the relationship between the base length and the side length of the second triangle.<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-140.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 140\" width=\"179\" height=\"119\" \/><br \/>\nIt is given that the graph shows the relationship between the base length x and the side length (of the two equal sides) y of an isosceles triangle in meters. The perimeter of a second isosceles triangle is 8 meters more than the perimeter of the first triangle.<br \/>\nNow,<br \/>\nFrom the graph,<br \/>\nThe equation for the first Isosceles triangle is:<br \/>\ny = 6 &#8211; \\(\\frac{1}{2}\\)x<br \/>\nMultiply by 2 into both sides<br \/>\n2y = 6 (2) &#8211; x<br \/>\n2y = 12 &#8211; x<br \/>\n2y + x = 12<br \/>\nThe above equation represents the perimeter of the first Isosceles triangle<br \/>\nWhere,<br \/>\nx is the base length<br \/>\ny is the side of the equal length like the third side<br \/>\nIt is also given that the perimeter of a second isosceles triangle is 8 meters more than the perimeter of the first triangle.<br \/>\nSo,<br \/>\n2y + x = 12 + 8<br \/>\n2y + x = 20<br \/>\nThe above equation represents the perimeter of the second Isosceles triangle<br \/>\nHence,<br \/>\nThe representation of the perimeter of the second isosceles triangle in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-65.png\" alt=\"\" width=\"480\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-65.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-65-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-65-150x150.png 150w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>b. How does the graph in part (a) compare to the graph shown?<br \/>\nAnswer:<br \/>\nThe equation of the perimeter of the first isosceles triangle is:<br \/>\ny = 6 &#8211; \\(\\frac{1}{2}\\)x<br \/>\nThe equation of the perimeter of the second isosceles triangle is:<br \/>\ny = 10 &#8211; \\(\\frac{1}{2}\\)x<br \/>\nHence,<br \/>\nFrom comparing the above 2 equations with the standard form of the linear equation<br \/>\ny = mx + c<br \/>\nWe can observe that the slopes are equal and only the y-intercepts are different<br \/>\nHence, from the above,<br \/>\nWe can conclude that the graphs of the perimeters of the first isosceles triangle and the second isosceles triangle are parallel<\/p>\n<p>Question 45.<br \/>\n<b>ANALYZING EQUATIONS<\/b><br \/>\nDetermine which of the equations could be represented by each graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-141.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 141\" width=\"353\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-141.png 353w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-141-209x300.png 209w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 45\" width=\"593\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-45.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-45-300x129.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend says that you can write the equation of any line in slope-intercept form. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\nNo, your friend is not correct<\/p>\n<p>Explanation:<br \/>\nWe can write the equation in slope-intercept form only when hat equation is in the linear form i.e., only x and y terms.<br \/>\nIf there are exponential terms in an equation, then we can not write that equation in slope-intercept form<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p>Question 47.<br \/>\n<b>WRITING<\/b><br \/>\nWrite the definition of the slope of a line in two different ways.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 47\" width=\"586\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-47.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-47-300x109.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nYour family goes on vacation to a beach 300 miles from your house. You reach your destination 6 hours after departing. Draw a graph that describes your trip. Explain what each part of your graph represents.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>ANALYZING A GRAPH<\/b><br \/>\nThe graphs of the functions g(x) = 6x + a and h(x) = 2x + b, where a and b are constants, are shown. They intersect at the point (p, q).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-142.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 142\" width=\"178\" height=\"160\" \/><br \/>\na. Label the graphs of g and h.<br \/>\nb. What do a and b represent?<br \/>\nc. Starting at the point (p, q), trace the graph of g until you get to the point with the x-coordinate p + 2. Mark this point C. Do the same with the graph of h. Mark this point D. How much greater is the y-coordinate of point C than the y-coordinate of point D?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 49.1\" width=\"583\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.1.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.1-300x164.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 49.2\" width=\"581\" height=\"550\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.2.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-49.2-300x284.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Your commute to school by walking and by riding a bus. The graph represents your commute.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-143.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 143\" width=\"209\" height=\"168\" \/><br \/>\na. Describe your commute in words.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-143.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 143\" width=\"209\" height=\"168\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that your commute to school is different at different time intervals<br \/>\nNow,<br \/>\nFrom 0 to 10 seconds,<br \/>\nThe distance you commuted gradually increases<br \/>\nFrom 10 to 14 seconds,<br \/>\nThe distance you commuted is constant<br \/>\nFrom 14 to 18 seconds,<br \/>\nThe distance you commuted abruptly increased<\/p>\n<p>b. Calculate and interpret the slopes of the different parts of the graph.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-143.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 143\" width=\"209\" height=\"168\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that there are different commutes at different time intervals,<br \/>\nNow,<br \/>\nThe x-axis represents the time<br \/>\nThe y-axis represents the distance in miles<br \/>\nNow,<br \/>\nFrom 0 to 10 seconds,<br \/>\nThe ordered pairs from the coordinate plane are:<br \/>\n(0, 0), (10, 0.5)<br \/>\nWe know that,<br \/>\nThe slope when 2 ordered pairs are given is represented as:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nFrom 0 to 10 seconds,<br \/>\nm = \\(\\frac{0.5 &#8211; 0}{10 &#8211; 0}\\)<br \/>\nm = \\(\\frac{0.5}{10}\\)<br \/>\nm = \\(\\frac{5}{100}\\)<br \/>\nm = 0.05<br \/>\nFrom 10 to 14 seconds,<br \/>\nThe ordered pairs from the coordinate plane are:<br \/>\n(10, 0.5), (14, 0.5)<br \/>\nWe know that,<br \/>\nThe slope when 2 ordered pairs are given is represented as:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nFrom 10 to 14 seconds,<br \/>\nm = \\(\\frac{0.5 &#8211; 0.5}{14 &#8211; 10}\\)<br \/>\nm = \\(\\frac{0}{4}\\)<br \/>\nm = 0<br \/>\nFrom 14 to 18 seconds,<br \/>\nThe ordered pairs from the coordinate plane are:<br \/>\n(14, 0.5), (18, 2.5)<br \/>\nWe know that,<br \/>\nThe slope when 2 ordered pairs are given is represented as:<br \/>\nm = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\nFrom 14 to 18 seconds,<br \/>\nm = \\(\\frac{2.5 &#8211; 0.5}{18 &#8211; 14}\\)<br \/>\nm = \\(\\frac{2}{4}\\)<br \/>\nm = \\(\\frac{1}{2}\\)<br \/>\nm = 0.5<br \/>\nHence, fromthe above,<br \/>\nWe can conclude that<br \/>\nThe slope from 0 to 10 seconds is: 0.05<br \/>\nThe slope from 10 to 14 seconds is: 0<br \/>\nThe slope from 14 to 18 seconds is: 0.5<\/p>\n<p><b>PROBLEM-SOLVING<br \/>\nIn Exercises 51 and 52, find the value of k so that the graph of the equation has the given slope or y-intercept.<\/b><\/p>\n<p>Question 51.<br \/>\ny = 4kx &#8211; 5; m = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 51\" width=\"151\" height=\"112\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-144.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 144\" width=\"168\" height=\"47\" \/><br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + \\(\\frac{5}{6}\\)k<br \/>\nCompare the above equation with the standard representation of the linear equation.<br \/>\nWe know that,<br \/>\nThe standard representation of the linear equation is:<br \/>\ny = mx + b<br \/>\nOn comparison,<br \/>\nWe get,<br \/>\nm = &#8211;\\(\\frac{1}{3}\\) and b = \\(\\frac{5}{6}\\)k<br \/>\nIt is given that<br \/>\nThe value of b is: -10<br \/>\nSo,<br \/>\n\\(\\frac{5}{6}\\)k = -10<br \/>\n5k = -10 \u00d7 6<br \/>\nk = \\(\\frac{-10 \u00d7 6}{5}\\)<br \/>\nk = -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of k is: -12<\/p>\n<p>Question 53.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nTo show that the slope of a line is constant, let (x<sub>1<\/sub>, y<sub>1<\/sub>) and (x<sub>2<\/sub>, y<sub>2<\/sub>) be any two points on the line y = mx + b. Use the equation of the line to express y<sub>1<\/sub> in terms of x<sub>1<\/sub> and y<sub>2<\/sub> in terms of x<sub>2<\/sub>. Then use the slope formula to show that the slope between the points is m.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 53\" width=\"337\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-53.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-53-252x300.png 252w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Find the coordinates of the figure after the transformation.<\/b><\/p>\n<p>Question 54.<br \/>\nTranslate the rectangle with 4 units left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-145.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 145\" width=\"170\" height=\"159\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-145.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 145\" width=\"170\" height=\"159\" \/><br \/>\nFrom the given graph,<br \/>\nThe rectangle is covered up to 1 to 3 units at the x-axis and 0 to -4 units at the y-axis<br \/>\nSo,<br \/>\nWhen we move the rectangle 4 units left, i.e., move the 1 and 3 units left for 4 units and move the 0 and -4 units left for 4 units<br \/>\nSo,<br \/>\nThe new rectangle in the graph is formed at:<br \/>\nAt the x-axis:<br \/>\n1 &#8211; 4 = -3<br \/>\n3 &#8211; 4 = -1<br \/>\nAt the y-axis:<br \/>\n0 &#8211; 4 = -4<br \/>\n-4 &#8211; 4 = -8<br \/>\nHence,<br \/>\nThe new rectangle is formed at (-1, -3) at the x-axis and at (-4, -8) at the y-axis<br \/>\nHence,<br \/>\nThe representation of the rectangle after the transformation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-61352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30.jpg\" alt=\"\" width=\"389\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30.jpg 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-30-300x286.jpg 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 55.<br \/>\nDilate the triangle with respect to the origin using a scale factor of 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-146.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 146\" width=\"168\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 55\" width=\"580\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-55.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-55-300x154.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 56.<br \/>\nReflect the trapezoid in the y-axis.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-147.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 147\" width=\"180\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<b>Determine whether the equation represents a linear or nonlinear function. Explain.<\/b><\/p>\n<p>Question 57.<br \/>\ny &#8211; 9 = \\(\\frac{2}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 57\" width=\"499\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-57.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-57-300x51.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 58.<br \/>\nx = 3 + 15y<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nx = 3 + 15y<br \/>\nRewrite the above given function in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\n15y = 3 &#8211; x<br \/>\ny = \\(\\frac{3 &#8211; x}{15}\\)<br \/>\ny = \\(\\frac{3}{15}\\) &#8211; \\(\\frac{1}{15}\\)x<br \/>\nHence,<br \/>\nThe above function is in the form of<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given function is linear<\/p>\n<p>Question 59.<br \/>\n\\(\\frac{x}{4}\\) + \\(\\frac{y}{12}\\) = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.5 Question 59\" width=\"550\" height=\"449\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-59.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.5-Question-59-300x245.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 60.<br \/>\ny = 3x<sup>4<\/sup> &#8211; 6<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 3x<sup>4<\/sup> &#8211; 6<br \/>\nRewrite the above given function in the form of<br \/>\ny = mx + c<br \/>\nBut,<br \/>\nThe above function is not in the form of<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given function is non-linear<\/p>\n<h3><a id=\"Lesson_3.6_Transformations_of_Graphs_of_Linear_Functions\"><\/a>Lesson 3.6 Transformations of Graphs of Linear Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow does the graph of the linear function f(x) = x compare to the graphs of g(x) = f(x) + c and h(x) = f(cx)? Comparing Graphs of Functions<br \/>\nAnswer:<br \/>\nThe given linear function is:<br \/>\nf (x) = x<br \/>\nThe graph corresponding to the above function will be the vertical line<br \/>\nNow,<br \/>\nThe given functions are:<br \/>\ng (x) = f (x) + c and h (x) = f (cx)<br \/>\nNow,<br \/>\nThe graph of g (x) will be the vertical line translated i.e., addition or subtraction by c units<br \/>\nThe graph of h (x) will be the graph of the function f(x) stretched or compressed by 1\/c units<br \/>\n<b><\/b><\/p>\n<p><b>EXPLORATION 1<br \/>\nComparing Graphs of Functions<br \/>\nWork with a partner. <\/b>The graph of f(x) = x is shown. Sketch the graph of each function, along with f, on the same set of coordinate axes. Use a graphing calculator to check your results. What can you conclude?<br \/>\na. g(x) = x + 4<br \/>\nb. g(x) = x + 2<br \/>\nc. g(x) = x &#8211; 2<br \/>\nd. g(x) = x &#8211; 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-148.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 148\" width=\"221\" height=\"199\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-149.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 149\" width=\"184\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\na. g(x) = x + 4<br \/>\nb. g(x) = x + 2<br \/>\nc. g(x) = x \u2013 2<br \/>\nd. g(x) = x \u2013 4<br \/>\nThe other given function is:<br \/>\nf (x) = x<br \/>\nNow,<br \/>\na.<br \/>\nThe given function is:<br \/>\ng (x) = x + 4<br \/>\nHence,<br \/>\nThe representations of f(x) and g (x) in the same coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-74.png\" alt=\"\" width=\"483\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-74.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-74-293x300.png 293w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translated 4 units away from f(x) to the left side i.e., towards the positive y-axis<\/p>\n<p>b.<br \/>\nThe given function is:<br \/>\ng (x) = x + 2<br \/>\nHence,<br \/>\nThe representations of f(x) and g (x) in the same coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-75.png\" alt=\"\" width=\"490\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-75.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-75-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-75-150x150.png 150w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translated 2 units away from f(x) to the left side i.e., towards the positive y-axis<\/p>\n<p>c.<br \/>\nThe given function is:<br \/>\ng (x) = x &#8211; 2<br \/>\nHence,<br \/>\nThe representations of f(x) and g (x) in the same coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-76.png\" alt=\"\" width=\"485\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-76.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-76-295x300.png 295w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translated 2 units away from f(x) to the right side i.e., towards the negative y-axis<\/p>\n<p>d,<br \/>\nThe given function is:<br \/>\ng (x) = x &#8211; 4<br \/>\nHence,<br \/>\nThe representations of f(x) and g (x) in the same coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-77.png\" alt=\"\" width=\"485\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-77.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-77-294x300.png 294w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translated 4 units away from f(x) to the right side i.e., towards the negative y-axis<\/p>\n<p><b>EXPLORATION 2<br \/>\nComparing Graphs of Functions<br \/>\nWork with a partner.<\/b> Sketch the graph of each function, along with f(x) = x, on the same set of coordinate axes. Use a graphing calculator to check your results. What can you conclude?<br \/>\na. h(x) = \\(\\frac{1}{2}\\)x<br \/>\nb. h(x) = 2x<br \/>\nc. h(x) = &#8211;\\(\\frac{1}{2}\\)x<br \/>\nd. h(x) = -2x<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\na. h(x) = \\(\\frac{1}{2}\\)x<br \/>\nb. h(x) = 2x<br \/>\nc. h(x) = &#8211;\\(\\frac{1}{2}\\)x<br \/>\nd. h(x) = -2x<br \/>\nThe other given function is:<br \/>\nf (x) = x<br \/>\nNow,<br \/>\na.<br \/>\nThe given function is:<br \/>\nh(x) = \\(\\frac{1}{2}\\)x<br \/>\nHence,<br \/>\nThe representations of f (x) and h (x) in the same coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-78.png\" alt=\"\" width=\"491\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-78.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-78-286x300.png 286w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) and f (x) passes through the origin and h (x) is steeper than f (x)<\/p>\n<p>b.<br \/>\nThe given function is:<br \/>\nh(x) = 2x<br \/>\nHence,<br \/>\nThe representation of f (x) and h(x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-79.png\" alt=\"\" width=\"479\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-79.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-79-288x300.png 288w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h(x) and f(x) passes through the origin and f (x) is steeper than h (x)<\/p>\n<p>c.<br \/>\nThe given function is:<br \/>\nh(x) = &#8211;\\(\\frac{1}{2}\\)x<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-80.png\" alt=\"\" width=\"580\" height=\"535\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-80.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-80-300x277.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) and f (x) are on the opposite axes<\/p>\n<p>d.<br \/>\nThe given function is:<br \/>\nh(x) = -2x<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-81.png\" alt=\"\" width=\"488\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-81.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-81-295x300.png 295w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and h (x) are in the opposite axes<\/p>\n<p><b>EXPLORATION 3<br \/>\nMatching Functions with Their Graphs<br \/>\nWork with a partner.<\/b> Match each function with its graph. Use a graphing calculator to check your results. Then use the results of Explorations 1 and 2 to compare the graph of k to the graph of f(x) = x.<br \/>\na. k(x) = 2x &#8211; 4<br \/>\nb. k(x) = -2x + 2<br \/>\nc. k(x) = &#8211;\\(\\frac{1}{2}\\)x + 4<br \/>\nd. k(x) = &#8211;\\(\\frac{1}{2}\\)x \u2014 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-150.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 150\" width=\"460\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-150.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-150-300x176.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\na. k(x) = 2x &#8211; 4<br \/>\nb. k(x) = -2x + 2<br \/>\nc. k(x) = &#8211;\\(\\frac{1}{2}\\)x + 4<br \/>\nd. k(x) = &#8211;\\(\\frac{1}{2}\\)x \u2014 2<br \/>\nThe other given function is:<br \/>\nf (x) = x<br \/>\nNow,<br \/>\na.<br \/>\nThe given equation is:<br \/>\nk(x) = 2x &#8211; 4<br \/>\nHence,<br \/>\nThe representation of k (x) and f (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-82.png\" alt=\"\" width=\"484\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-82.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-82-295x300.png 295w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph C) matches k (x)<br \/>\nBy comparing f (x) and k (x),<br \/>\nWe can say that k (x) translates 2 units from f (x) towards the positive x-axis<\/p>\n<p>b.<br \/>\nThe given function is:<br \/>\nk(x) = -2x + 2<br \/>\nHence,<br \/>\nThe representation of k (x) and f (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-83.png\" alt=\"\" width=\"479\" height=\"494\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-83.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-83-291x300.png 291w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph A) matches k (x)<br \/>\nBy comparing f (x) and k (x),<br \/>\nWe can say that k (x) and f (x) are on the opposite axes<\/p>\n<p>c.<br \/>\nThe given function is:<br \/>\nk(x) = &#8211;\\(\\frac{1}{2}\\)x + 4<br \/>\nHence,<br \/>\nThe representation of k (x) and f (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-84.png\" alt=\"\" width=\"493\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-84.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-84-283x300.png 283w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph D) matches k (x)<br \/>\nBy comparing f (x) and k (x),<br \/>\nWe can say that k (x) and f (x) are on opposite axes and k (x) only translates through only the positive and negative x-axes<\/p>\n<p>d.<br \/>\nThe given function is:<br \/>\nk(x) = &#8211;\\(\\frac{1}{2}\\)x \u2014 2<br \/>\nHence,<br \/>\nThe representation of k (x) and f (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-85.png\" alt=\"\" width=\"497\" height=\"517\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-85.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-85-288x300.png 288w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph B) matches k (x)<br \/>\nBy comparing f (x) and k (x),<br \/>\nWe can say that k (x) and f(x) are on the opposite axes and k (x) translates through only the negative x-axis and the negative y-axis<\/p>\n<p><b style=\"font-style: inherit;\">Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow does the graph of the linear function f(x) = x compare to the graphs of g(x) = f(x) + c and h(x) = f(cx)?<br \/>\nAnswer:<br \/>\nThe given linear function is:<br \/>\nf (x) = x<br \/>\nThe graph corresponding to the above function will be the vertical line<br \/>\nNow,<br \/>\nThe given functions are:<br \/>\ng (x) = f (x) + c and h (x) = f (cx)<br \/>\nNow,<br \/>\nThe graph of g (x) will be the vertical line translated i.e., addition or subtraction by c units<br \/>\nThe graph of h (x) will be the graph of the function f(x) stretched or compressed by 1\/c units<b><\/b><\/p>\n<p><b>3.6 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<br \/>\nUsing f, graph (a) g and (b) h. Describe the transformations from the graph of f to the graphs of g and h.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = 3x + 1; g(x) = f(x) &#8211; 2; h(x) = f(x &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 1; g (x) = f (x) &#8211; 2 and h (x) = f (x &#8211; 2)<br \/>\nNow,<br \/>\nIt is given that,<br \/>\ng (x) = f (x) &#8211; 2<br \/>\nSo,<br \/>\ng (x) = 3x + 1 &#8211; 2<br \/>\ng (x) = 3x &#8211; 1<br \/>\nIt is given that,<br \/>\nh (x) = f (x &#8211; 2)<br \/>\nh (x) = 3 (x &#8211; 2) + 1<br \/>\nh (x) = 3 (x) + 3 (2) + 1<br \/>\nh (x) = 3x + 6 + 1<br \/>\nh (x) = 3x + 7<br \/>\nHence,<br \/>\nThe representations of f (x), g (x), and h (x) in a coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-86.png\" alt=\"\" width=\"483\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-86.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-86-290x300.png 290w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\ng (x) is translated 2 units away from f (x) toward the positive x-axis and h (x) is translated 5 units away from f (x) toward the positive y-axis<\/p>\n<p>Question 2.<br \/>\nf(x) = -4x &#8211; 2; g(x) = -f(x); h(x) = f(-x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -4x &#8211; 2; g (x) = -f (x) and h (x) = f (-x)<br \/>\nNow,<br \/>\nIt is given that,<br \/>\ng (x) = -f (x)<br \/>\nSo,<br \/>\ng (x) = &#8211; (-4x &#8211; 2)<br \/>\ng (x) = 4x + 2<br \/>\nIt is given that,<br \/>\nh (x) = f (-x)<br \/>\nh (x) = -4 (-x) &#8211; 2<br \/>\nh (x) = 4x &#8211; 2<br \/>\nHence,<br \/>\nThe representations of f (x), g (x), and h (x) in a coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-62998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-87.png\" alt=\"\" width=\"484\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-87.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-87-293x300.png 293w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\ng (x) is translated 2.5 units away from f (x) toward the positive y-axis and h (x) is translated 1 unit away from f (x) toward the positive x-axis<\/p>\n<p><b>Using f, graph (a) g and (b) h. Describe the transformations from the graph of f to the graphs of g and h.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = 4x &#8211; 2; g(x) = f (\\(\\frac{1}{2}\\)x ); h(x) = 2f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 4x &#8211; 2; g (x) = f (\\(\\frac{1}{2}\\)x ) and h (x) = 2f (x)<br \/>\nNow,<br \/>\nIt is given that,<br \/>\ng (x) = f (\\(\\frac{1}{2}\\)x )<br \/>\nSo,<br \/>\ng (x) = 4 ( f (\\(\\frac{1}{2}\\)x ) &#8211; 2<br \/>\ng (x) = 2x &#8211; 2<br \/>\nIt is given that,<br \/>\nh (x) = 2f (x)<br \/>\nh (x) = 2 (4x &#8211; 2)<br \/>\nh (x) = 2 (4x) &#8211; 2(2)<br \/>\nh (x) = 8x &#8211; 4<br \/>\nHence,<br \/>\nThe representations of f (x), g (x), and h (x) in a coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-88.png\" alt=\"\" width=\"496\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-88.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-88-296x300.png 296w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\ng (x) is translated 0.5 units away from f (x) toward the positive x-axis and h (x) is translated 0 units away from f (x) toward the origin<\/p>\n<p>Question 4.<br \/>\nf(x) = -3x + 4; g(x) = f(2x); h(x) = \\(\\frac{1}{2}\\)f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -3x + 4; g (x) = f (2x) and h (x) = \\(\\frac{1}{2}\\)f(x)<br \/>\nNow,<br \/>\nIt is given that,<br \/>\ng (x) = f (2x)<br \/>\nSo,<br \/>\ng (x) = -3 (2x) + 4<br \/>\ng (x) = -6x + 4<br \/>\nIt is given that,<br \/>\nh (x) = \\(\\frac{1}{2}\\)f(x)<br \/>\nh (x) = \\(\\frac{1}{2}\\) (3x + 4)<br \/>\nh (x) = \\(\\frac{3}{2}\\)x + \\(\\frac{4}{2}\\)<br \/>\nh (x) = \\(\\frac{3}{2}\\)x + 2<br \/>\nHence,<br \/>\nThe representations of f (x), g (x), and h (x) in a coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-89.png\" alt=\"\" width=\"502\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-89.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-89-291x300.png 291w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\ng (x) and f (x) are on the same axis and h (x) and f (x) are on the opposite axis<\/p>\n<p>Q<span style=\"font-size: 16px;\">uestion 5.<br \/>\n<\/span>Graph f(x) = x and h(x) = \\(\\frac{1}{2}\\)x &#8211; 2. Describe the transformations from the graph of f to the graph of h.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = x and h (x) = \\(\\frac{1}{2}\\)x &#8211; 2<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-90.png\" alt=\"\" width=\"502\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-90.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-90-285x300.png 285w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) translated 4 units away from f (x) towards the positive x-axis<\/p>\n<h3><a id=\"Transformations_of_Graphs_of_Linear_Functions_3.6_Exercises\"><\/a>Transformations of Graphs of Linear Functions 3.6 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nDescribe the relationship between f(x) = x and all other nonconstant linear functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 1\" width=\"581\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-1-300x72.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b><br \/>\nName four types of transformations. Give an example of each and describe how it affects the graph of a function.<br \/>\nAnswer:<br \/>\nThe four types of transformations that affect the graph of a function are:<br \/>\na. Translation<br \/>\nEx:<br \/>\nf (x) = x and g (x) = 2 f(x)<br \/>\nb. Rotation<br \/>\nEx:<br \/>\nf (x) = 3x + 2 and g (x) = 3x &#8211; 2<br \/>\nc. Reflection<br \/>\nEx:<br \/>\nf (x) =x and g (x) =-f (x)<br \/>\nd. Dilation<br \/>\nEx:<br \/>\nf (x) = 3x + 6 and g (x) = f (2x)<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b><br \/>\nHow does the value of a in the equation y = f(ax) affect the graph of y = f(x)? How does the value of a in the equation y = af(x) affect the graph of y = f(x)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-151.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 151\" width=\"195\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 3\" width=\"569\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-3.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-3-300x89.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>REASONING<\/b><br \/>\nThe functions f and g are linear functions. The graph of g is a vertical shrink of the graph of f. What can you say about the x-intercepts of the graphs of f and g? Is this always true? Explain.<br \/>\nAnswer:<br \/>\nIt is given that the functions f and g are linear functions<br \/>\nWe know that,<br \/>\nf can be written as f (x)<br \/>\ng can be written as g (x)<br \/>\nIt is also given that the graph of g is a vertical shrink of the graph of f.<br \/>\nSo,<br \/>\nSince the graph of g shrinks, then the x-intercept of g will also shrink if we observe the functions of f and g<br \/>\nHence, from the above,<br \/>\nWe can conclude that the x-intercept of g will shrink and this is always true<\/p>\n<p><b>In Exercises 5\u201310, use the graphs of f and g to describe the transformation from the graph of f to the graph of g.<\/b><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-152.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 152\" width=\"160\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 5\" width=\"562\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-5.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-5-300x47.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 153\" width=\"162\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153.png 162w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153-150x150.png 150w\" sizes=\"(max-width: 162px) 100vw, 162px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 153\" width=\"162\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153.png 162w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-153-150x150.png 150w\" sizes=\"(max-width: 162px) 100vw, 162px\" \/><br \/>\nFrom the above graph,<br \/>\nThe given functions are:<br \/>\nf (x) = x &#8211; 3<br \/>\ng (x) = f (x + 4)<br \/>\nSo,<br \/>\ng (x) = (x + 4) &#8211; 3<br \/>\ng (x) = x + 1<br \/>\nHence,<br \/>\nWhen we observe f (x) and g (x), we can say that<br \/>\ng (x) shrinks by 2 units of f (x)<\/p>\n<p>Question 7.<br \/>\nf(x) = \\(\\frac{1}{3}\\)x + 3; g(x) = f(x) = -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 7\" width=\"560\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-7.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-7-300x164.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = -3x + 4; g(x) = f(x) + 1<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -3x + 4<br \/>\ng (x) = f (x) + 1<br \/>\nSo,<br \/>\ng (x) = -3x + 4 + 1<br \/>\ng (x) = -3x + 5<br \/>\nHence,<br \/>\nThe representation of f and g in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-118.png\" alt=\"\" width=\"485\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-118.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-118-294x300.png 294w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates 1 unit away from f (x)<\/p>\n<p>Question 9.<br \/>\nf(x) = -x &#8211; 2; g(x) = f(x + 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 9\" width=\"561\" height=\"324\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-9.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-9-300x173.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x &#8211; 5; g(x) = f(x &#8211; 3)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = \\(\\frac{1}{2}\\)x &#8211; 5<br \/>\ng (x) = f (x &#8211; 3)<br \/>\nSo,<br \/>\ng (x) = \\(\\frac{1}{2}\\) ( x &#8211; 3 ) &#8211; 5<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-119.png\" alt=\"\" width=\"516\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-119.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-119-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-119-150x150.png 150w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) is dilated from f (x)<\/p>\n<p>Question 11.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou and a friend start biking from the same location. Your distance d (in miles) after t minutes is given by the function d(t) = \\(\\frac{1}{5}\\)t. Your friend starts biking 5 minutes after you. Your friend\u2019s distance f is given by the function f(t) = d(t &#8211; 5). Describe the transformation from the graph of d to the graph of f.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-154.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 154\" width=\"104\" height=\"189\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 11\" width=\"574\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-11.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-11-300x171.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 12.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe total cost C (in dollars) to cater an event with p people is given by the function C(p) = 18p + 50. The set-up fee increases by $25. The new total cost T is given by the function T(p) = C(p) + 25. Describe the transformation from the graph of C to the graph of T.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-155.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 155\" width=\"232\" height=\"172\" \/><br \/>\nAnswer:<br \/>\nIt is given that the total cost C (in dollars) to cater an event with p people is given by the function<br \/>\nC(p) = 18p + 50<br \/>\nIt is also given that the set-up fee increases by $25.<br \/>\nSo,<br \/>\nThe new total cost T is given by the function<br \/>\nT(p) = C(p) + 25<br \/>\nSo,<br \/>\nT (p) = 18p + 50 + 25<br \/>\nT (p) = 18p + 75<br \/>\nHence,<br \/>\nThe representation of T (p) and C (p) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-120.png\" alt=\"\" width=\"495\" height=\"489\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-120.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-120-300x296.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that T (p) translated 25 units away from C (p)<\/p>\n<p><b>In Exercises 13\u201316, use the graphs of f and h to describe the transformation from the graph of f to the graph of h.<\/b><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-156.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 156\" width=\"147\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 13\" width=\"542\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-13.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-13-300x20.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-157.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 157\" width=\"161\" height=\"159\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-157.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 157\" width=\"161\" height=\"159\" \/><br \/>\nFrom the above graph,<br \/>\nThe given functions are:<br \/>\nf (x) = -3x + 1<br \/>\nh (x) = f (-x)<br \/>\nSo,<br \/>\nh (x) = -3 (-x) + 1<br \/>\nh (x) = 3x + 1<br \/>\nHence,<br \/>\nThe representations of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-116.png\" alt=\"\" width=\"488\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-116.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-116-293x300.png 293w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and h (x) are perpendicular lines<\/p>\n<p>Question 15.<br \/>\nf(x) = -5 &#8211; x; h(x) = f(-x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 15\" width=\"560\" height=\"417\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-15.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-15-300x223.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = \\(\\frac{1}{4}\\)x &#8211; 2; h(x) = -f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = \\(\\frac{1}{4}\\)x &#8211; 2<br \/>\nh (x) = &#8211; f(x)<br \/>\nSo,<br \/>\nh (x) = &#8211; (\\(\\frac{1}{4}\\)x &#8211; 2)<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-117.png\" alt=\"\" width=\"499\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-117.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-117-287x300.png 287w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) is a reflection of f (x) on the y-axis<\/p>\n<p><b>In Exercises 17\u201322, use the graphs of f and r to describe the transformation from the graph of f to the graph of r.<\/b><\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-158.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 158\" width=\"141\" height=\"161\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 17\" width=\"581\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-17.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-17-300x33.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 159\" width=\"159\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159.png 159w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159-150x150.png 150w\" sizes=\"(max-width: 159px) 100vw, 159px\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 159\" width=\"159\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159.png 159w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-159-150x150.png 150w\" sizes=\"(max-width: 159px) 100vw, 159px\" \/><br \/>\nFrom the above graph,<br \/>\nThe given functions are:<br \/>\nf (x) = -x<br \/>\nr (x) = f (\\(\\frac{1}{4}\\) x)<br \/>\nSo,<br \/>\nr (x) = &#8211;\\(\\frac{1}{4}\\)x<br \/>\nHence,<br \/>\nThe representation of f (x) and r (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-113.png\" alt=\"\" width=\"495\" height=\"526\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-113.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-113-282x300.png 282w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that r (x) shrinks by \\(\\frac{1}{4}\\) of f (x)<\/p>\n<p>Question 19.<br \/>\nf(x) = -2x &#8211; 4; r(x) = f(\\(\\frac{1}{2}\\)x )<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 19\" width=\"538\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-19.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-19-300x263.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = 3x + 5; r(x) = f (\\(\\frac{1}{3}\\)x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 5<br \/>\nr (x) = f (\\(\\frac{1}{3}\\)x)<br \/>\nSo,<br \/>\nr (x) = 3 ( \\(\\frac{1}{3}\\) x ) + 5<br \/>\nr (x) = x + 5<br \/>\nHence,<br \/>\nThe representation of f (x) and r (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-114.png\" alt=\"\" width=\"488\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-114.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-114-293x300.png 293w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that r (x) shrinks by 1 unit of f (x)<\/p>\n<p>Question 21.<br \/>\nf(x) = \\(\\frac{2}{3}\\)x + 1; r(x) = 3f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 21\" width=\"585\" height=\"392\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-21.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-21-300x201.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = &#8211;\\(\\frac{1}{4}\\)x &#8211; 2; r(x) = 4f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = &#8211;\\(\\frac{1}{4}\\)x &#8211; 2<br \/>\nr (x) = 4 f (x)<br \/>\nSo,<br \/>\nr (x) = 4 [-\\(\\frac{1}{4}\\)x &#8211; 2]<br \/>\nr (x) = -x &#8211; 8<br \/>\nHence,<br \/>\nThe representation of f (x) and r (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-115.png\" alt=\"\" width=\"504\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-115.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-115-294x300.png 294w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that r (x) translates 4 units away from\u00a0 f (x)<\/p>\n<p><b>In Exercises 23\u201328, use the graphs of f and h to describe the transformation from the graph of f to the graph of h.<\/b><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-160.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 160\" width=\"147\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 23\" width=\"542\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-23.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-23-300x37.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-161.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 161\" width=\"152\" height=\"166\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-161.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 161\" width=\"152\" height=\"166\" \/><br \/>\nFrom the above grah,<br \/>\nThe given functions are:<br \/>\nf (x) = -2x &#8211; 6<br \/>\nh (x) = \\(\\frac{1}{3}\\) f(x)<br \/>\nSo,<br \/>\nh (x) = &#8211;\\(\\frac{1}{3}\\) (2x + 6)<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-110.png\" alt=\"\" width=\"489\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-110.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-110-284x300.png 284w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) stretches by \\(\\frac{1}{3}\\) of f (x)<\/p>\n<p>Question 25.<br \/>\nf(x) = 3x &#8211; 12; h(x) = \\(\\frac{1}{6}\\)f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 25\" width=\"509\" height=\"456\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-25.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-25-300x269.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = -x + 1; h(x) = f(2x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -x + 1<br \/>\nh (x) = f (2x)<br \/>\nSo,<br \/>\nh (x) = -(2x) + 1<br \/>\nh (x) = -2x + 1<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-111.png\" alt=\"\" width=\"482\" height=\"492\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-111.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-111-294x300.png 294w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) stretches by 1 unit from f (x)<\/p>\n<p>Question 27.<br \/>\nf(x) = -2x &#8211; 2; h(x) = f(5x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 27\" width=\"539\" height=\"449\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-27.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-27-300x250.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = 4x + 8; h(x) = \\(\\frac{3}{4}\\)f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 4x + 8<br \/>\nh (x) = \\(\\frac{3}{4}\\) f (x)<br \/>\nSo,<br \/>\nh (x) = \\(\\frac{3}{4}\\) (4x + 8)<br \/>\nh (x) = \\(\\frac{3}{4}\\) (4x) + \\(\\frac{3}{4}\\) (8)<br \/>\nh (x) = 3x + 6<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-112.png\" alt=\"\" width=\"479\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-112.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-112-290x300.png 290w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) shrinks by 2 units from f (x)<\/p>\n<p><b>In Exercises 29\u201334, use the graphs of f and g to describe the transformation from the graph of f to the graph of g.<\/b><\/p>\n<p>Question 29.<br \/>\nf(x) = x &#8211; 2; g(x) = \\(\\frac{1}{4}\\)f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 29\" width=\"513\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-29.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-29-300x261.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 30.<br \/>\nf(x) = -4x + 8; g(x) = -f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -4x + 8<br \/>\ng (x) = -f (x)<br \/>\nSo,<br \/>\ng (x) = -4 (-x) + 8<br \/>\ng (x) = 4x + 8<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-107.png\" alt=\"\" width=\"481\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-107.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-107-293x300.png 293w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nHence, from the above graph,<br \/>\nWe can conclude that g (x) is a reflection of f (x)<\/p>\n<p>Question 31.<br \/>\nf(x) = -2x &#8211; 7; g(x) = f(x &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 31\" width=\"560\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-31.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-31-300x166.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 32.<br \/>\nf(x) = 3x + 8; g(x) = f(\\(\\frac{2}{3}\\)x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 8<br \/>\ng (x) = f (\\(\\frac{2}{3}\\)x)<br \/>\nSo,<br \/>\ng (x) = 3 ( \\(\\frac{2}{3}\\) ) x + 8<br \/>\ng (x) = 2x + 8<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-108.png\" alt=\"\" width=\"515\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-108.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-108-300x290.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) shrink by 1 unit of the graph of f (x)<\/p>\n<p>Question 33.<br \/>\nf(x) = x &#8211; 6; g(x) = 6f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 33\" width=\"576\" height=\"434\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-33.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-33-300x226.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 34.<br \/>\nf(x) = -x; g(x) = f(x) -3<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -x<br \/>\ng (x) = f (x) &#8211; 3<br \/>\nSo,<br \/>\ng (x) = -x &#8211; 3<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-109.png\" alt=\"\" width=\"482\" height=\"489\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-109.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-109-296x300.png 296w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) is translated by 3 units away from f (x)<\/p>\n<p><b>In Exercises 35\u201338, write a function g in terms of f so that the statement is true.<\/b><\/p>\n<p>Question 35.<br \/>\nThe graph of g is a horizontal translation 2 units right of the graph of f.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 35\" width=\"155\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-35.png 155w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-35-150x31.png 150w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/p>\n<p>Question 36.<br \/>\nThe graph of g is a reflection in the y-axis of the graph of f.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nf can be writen as f (x)<br \/>\ng can be written as g (x)<br \/>\nNow,<br \/>\nThe given statement is:<br \/>\nThe graph of g is a reflection of f(x) in the y-axis of the graph of f (x)<br \/>\nSo,<br \/>\nReflection in the y-axis means if f (x) is +ve, then the reflection of f (x) will be -ve and vice-versa<br \/>\nHence,<br \/>\nThe representation of the given statement in terms of f(x) is:<br \/>\ng (x) = f (-x)<\/p>\n<p>Question 37.<br \/>\nThe graph of g is a vertical stretch by a factor of 4 of the graph of f.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 37\" width=\"124\" height=\"34\" \/><\/p>\n<p>Question 38.<br \/>\nThe graph of g is a horizontal shrink by a factor of \\(\\frac{1}{5}\\) of the graph of f.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nf can be writen as f (x)<br \/>\ng can be written as g (x)<br \/>\nNow,<br \/>\nThe given statement is:<br \/>\nThe graph of g is a horizontal shrink by a factor of \\(\\frac{1}{5}\\) of the graph<br \/>\nWe know that,<br \/>\n&#8220;Shrink&#8221; is represented by &#8216;-&#8216;<br \/>\n&#8220;Stretch&#8221; is represented by &#8216;+&#8217;<br \/>\nHence,<br \/>\nThe representation of the given statement in terms of f (x) is:<br \/>\ng (x) = &#8211; \\(\\frac{1}{5}\\) f (x)<\/p>\n<p><b>ERROR ANALYSIS In Exercises 39 and 40, describe and correct the error in graphing g.<\/b><\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-162.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 162\" width=\"260\" height=\"202\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 39\" width=\"570\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-39.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-39-300x149.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-163.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 163\" width=\"280\" height=\"201\" \/><br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = -x + 3 and g (x) = f (-x)<br \/>\nSo,<br \/>\ng (x) = -[-x] + 3<br \/>\ng (x) = x + 3<br \/>\nHence,<br \/>\nThe representations of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-106.png\" alt=\"\" width=\"508\" height=\"490\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-106.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-106-300x289.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and g (x) are perpendicular lines from the graph<\/p>\n<p><b>In Exercises 41\u201346, graph f and h. Describe the transformations from the graph of f to the graph of h.<\/b><\/p>\n<p>Question 41.<br \/>\nf(x) = x; h(x) = \\(\\frac{1}{3}\\)x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 41\" width=\"522\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-41.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-41-300x176.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 42.<br \/>\nf(x) = x; h(x) = 4x &#8211; 2<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = x and h (x) = 4x &#8211; 2<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-103.png\" alt=\"\" width=\"491\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-103.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-103-296x300.png 296w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the transformations are a vertical stretch by a factor of 4 followed by a vertical translation of 2 units down<\/p>\n<p>Question 43.<br \/>\nf(x) = x; h(x) = -3x &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 43\" width=\"565\" height=\"324\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-43.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-43-300x172.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 44.<br \/>\nf(x) = x; h(x) = &#8211;\\(\\frac{1}{2}\\)x + 3<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = x and h (x) = &#8211;\\(\\frac{1}{2}\\)x + 3<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-104.png\" alt=\"\" width=\"496\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-104.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-104-285x300.png 285w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Hence, from the above,<br \/>\nWe can conclude that the transformations are a vertical shrink by a factor of \\(\\frac{1}{2}\\) followed by a vertical translation of 3 units up<\/p>\n<p>Question 45.<br \/>\nf(x) = 2x; h(x) = 6x &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 45\" width=\"590\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-45.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-45-300x151.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 46.<br \/>\nf(x) = 3x; h(x) = -3x &#8211; 7<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x and h (x) = -3x &#8211; 7<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-105.png\" alt=\"\" width=\"483\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-105.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-105-290x300.png 290w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the transformations are a vertical shrink by a factor of 3 followed by a vertical translation of 7 units down<\/p>\n<p>Question 47.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe function t(x) = -4x +72 represents the temperature from 5 P.M. to 11 P.M., where x is the number of hours after 5 P.M. The function d(x) = 4x + 72 represents the temperature from 10 A.M. to 4 P.M., where x is the number of hours after 10 A.M. Describe the transformation from the graph of t to the graph of d.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-164.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 164\" width=\"272\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 47\" width=\"601\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-47.png 601w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-47-300x181.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA school sells T-shirts to promote school spirit. The school\u2019s profit is given by the function P(x) = 8x &#8211; 150, where x is the number of T-shirts sold. During the playoffs, the school increases the price of the T-shirts. The school\u2019s profit during the play-offs is given by the function Q(x) = 16x &#8211; 200, where x is the number of T-shirts sold. Describe the transformations from the graph of P to the graph of Q.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-164.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 164.1\" width=\"368\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-164.1.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-164.1-300x165.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><br \/>\nAnswer:<br \/>\nIt is given that a school sells T-shirts to promote school spirit. The school\u2019s profit is given by the function<br \/>\nP(x) =8x- 150<br \/>\nwhere,<br \/>\nx is the number of T-shirts sold<br \/>\nIt is also given that during the playoffs, the school increases the price of the T-shirts. The school\u2019s profit during the play-offs is given by the function<br \/>\nQ(x) = 16x &#8211; 200<br \/>\nwhere,<br \/>\nx is the number of T-shirts sold.<br \/>\nHence,<br \/>\nThe representation of P (x) and Q(x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-102.png\" alt=\"\" width=\"479\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-102.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-102-288x300.png 288w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above graph,<br \/>\nWe can conclude that<br \/>\nThe x-axis shrink by a factor of 2<br \/>\nThe y-axis shrink by 50<\/p>\n<p>Question 49.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nThe graph of g(x) = a \u2022 f(x &#8211; b) + c is a transformation of the graph of the linear function f. Select the word or value that makes each statement true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-165.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 165\" width=\"235\" height=\"110\" \/><br \/>\na. The graph of g is a vertical ______ of the graph of f when a = 4, b = 0, and c = 0.<br \/>\nb. The graph of g is a horizontal translation ______ of the graph of f when a = 1, b = 2, and c = 0.<br \/>\nc. The graph of g is a vertical translation 1 unit up of the graph of f when a = 1, b = 0, and c = ____.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 49\" width=\"586\" height=\"184\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-49.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-49-300x94.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nThe graph of h(x) = a \u2022 f(bx &#8211; c) + d is a transformation of the graph of the linear function f. Select the word or value that makes each statement true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-166.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 166\" width=\"239\" height=\"100\" \/><br \/>\na. The graph of h is a ______ shrink of the graph of f when a = \\(\\frac{1}{3}\\), b = 1, c = 0, and d = 0.<br \/>\nb. The graph of h is a reflection in the ______ of the graph of f when a = 1, b = -1, c = 0, and d = 0.<br \/>\nc. The graph of h is a horizontal stretch of the graph of f by a factor of 5 when a = 1, b = _____, c = 0, and d = 0.<br \/>\nAnswer:<br \/>\nThe given original function is:<br \/>\nf (x) = x<br \/>\nThe given choice of words to make the given statements true is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-166.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 166\" width=\"239\" height=\"100\" \/><br \/>\nThe transformation of the function of f (x) is given as:<br \/>\nh (x) = a f (bx &#8211; c) + d<br \/>\nWhere,<br \/>\na, b, c, and d are constants<br \/>\nNow,<br \/>\na.<br \/>\nThe given values of constants are:<br \/>\na = \\(\\frac{1}{3}\\),<br \/>\nb = 1<br \/>\nc = 0<br \/>\nd = 0<br \/>\nSo,<br \/>\nh (x) = \\(\\frac{1}{3}\\)f (1 (x) &#8211; 0) + 0<br \/>\nh (x) = \\(\\frac{1}{3}\\) f (x)<br \/>\nSo,<br \/>\nh (x) = \\(\\frac{1}{3}\\)x<br \/>\nHence,<br \/>\nThe representations of f (x) and h (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-99.png\" alt=\"\" width=\"499\" height=\"519\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-99.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-99-288x300.png 288w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph of h is a vertical shrink of the graph of f when a = \\(\\frac{1}{3}\\), b = 1, c = 0, and d = 0.<\/p>\n<p>b.<br \/>\nThe given values of constants are:<br \/>\na = 1<br \/>\nb = -1<br \/>\nc = 0<br \/>\nd = 0<br \/>\nSo,<br \/>\nh (x) = 1f (-1 (x) &#8211; 0) + 0<br \/>\nh (x) =\u00a0 f (-x)<br \/>\nSo,<br \/>\nh (x) = -x<br \/>\nHence,<br \/>\nThe representations of f (x) and h (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-100.png\" alt=\"\" width=\"487\" height=\"492\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-100.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-100-297x300.png 297w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph of h is a reflection in the y-axis of the graph of f when a = 1, b = -1, c = 0, and d = 0<\/p>\n<p>c.<br \/>\nThe given values of constants are:<br \/>\na = 1<br \/>\nb = p<br \/>\nc = 0<br \/>\nd = 0<br \/>\nSo,<br \/>\nh (x) = 1f (p (x) &#8211; 0) + 0<br \/>\nh (x) =\u00a0 f (px)<br \/>\nSo,<br \/>\nh (x) = px<br \/>\nHence,<br \/>\nThe representations of f (x) and h (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-101.png\" alt=\"\" width=\"488\" height=\"517\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-101.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-101-283x300.png 283w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph of h is a horizontal stretch of the graph of f by a factor of 5 when a = 1, b = \\(\\frac{1}{5}\\), c = 0, and d = 0<\/p>\n<p>Question 51.<br \/>\n<b>ANALYZING GRAPHS<\/b><br \/>\nWhich of the graphs are related by only a translation? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-167.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 167\" width=\"349\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-167.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-167-255x300.png 255w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 51\" width=\"542\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-51.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-51-300x69.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nA swimming pool is filled with water by a hose at a rate of 1020 gallons per hour. The amount v (in gallons) of water in the pool after t hours is given by the function v(t) = 1020t. How does the graph of v change in each situation?<br \/>\na. A larger hose is found. Then the pool is filled at a rate of 1360 gallons per hour.<br \/>\nAnswer:<br \/>\nIt is given that a swimming pool is filled with water by a hose at a rate of 1020 gallons per hour. The amount v (in gallons) of water in the pool after t hours is given by the function<br \/>\nv(t) = 1020t<br \/>\nNow,<br \/>\nIt is also given that a pool is filled at a rate of 1360 gallons per hour<br \/>\nSo,<br \/>\nThe overall rate change = 1340 \/ 1020<br \/>\n= 440 \/ 330<br \/>\n= 4 \/ 3<br \/>\nSo,<br \/>\nThe new rate of change is representad by the function<br \/>\nf (t) = (4 \/ 3) v (t)<br \/>\nHence,<br \/>\nThe representation of the graph of v using the functions v (t) = 1020t and v (t) = 1360t is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-98.png\" alt=\"\" width=\"478\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-98.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-98-286x300.png 286w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>b. Before filling up the pool with a hose, a water truck adds 2000 gallons of water to the pool.<br \/>\nAnswer:<br \/>\nWe know that,<br \/>\nFrom part (a),<br \/>\nThe function for filling up the pool with a hose is given as:<br \/>\nv (t) = 1020t<br \/>\nIt is given that before filling up the pool with a hose, a water truck adds 2000 gallons of water to the pool<br \/>\nSo,<br \/>\nv (t) = 1020t + 2000<br \/>\nHence,<br \/>\nThe representations of the functions before filling the hose and\u00a0 a water truck adds 2000 gallons of water are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-97.png\" alt=\"\" width=\"488\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-97.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-97-295x300.png 295w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 53.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nYou have $50 to spend on fabric for a blanket. The amount m (in dollars) of money you have after buying y yards of fabric is given by the function m(y) = -9.98y + 50. How does the graph of m change in each situation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-168.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 168\" width=\"140\" height=\"101\" \/><br \/>\na. You receive an additional $10 to spend on the fabric.<br \/>\nb. The fabric goes on sale, and each yard now costs $4.99.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 53\" width=\"562\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-53.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-53-300x224.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nWrite a function g whose graph passes through the point (4, 2) and is a transformation of the graph of f(x) = x.<br \/>\nAnswer:<br \/>\nIt is given that a function g whose graph passes through the point (4, 2) and is a transformation of the graph of f(x) = x<br \/>\nWe know that,<br \/>\nThe equation that passes through (h, k) and it is a transformation of another function is:<br \/>\ny = fx &#8211; h) + k<br \/>\nSo,<br \/>\nFrom (4, 2)<br \/>\nAs the translation between the values of x and y in the given point is 2,<br \/>\nWe can make the value of &#8216;h&#8217; as -2<br \/>\nWe can make the value of k as -4<br \/>\nHence,<br \/>\nThe equation that passes through (4, 2) is:<br \/>\ny = (x + 2 ) &#8211; 4<br \/>\ny = x &#8211; 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the function that passes through (4, 2) is:<br \/>\ng (x) = x &#8211; 2<\/p>\n<p><b>In Exercises 55\u201360, graph f and g. Write g in terms of f. Describe the transformation from the graph of f to the graph of g.<\/b><\/p>\n<p>Question 55.<br \/>\nf(x) = 2x &#8211; 5; g(x) = 2x &#8211; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 55\" width=\"580\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-55.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-55-300x153.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 56.<br \/>\nf(x) = 4x + 1; g(x) = -4x &#8211; 1<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nf (x) = 4x + 1<br \/>\ng (x) = -4x &#8211; 1<br \/>\nSo,<br \/>\ng (x) = &#8211; (4x + 1)<br \/>\ng (x) = -f (x)<br \/>\nHence,<br \/>\nThe representations of f (x) and g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-93.png\" alt=\"\" width=\"479\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-93.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-93-290x300.png 290w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and g (x) are on the opposite quadrants<\/p>\n<p>Question 57.<br \/>\nf(x) = 3x + 9; g(x) = 3x + 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 57\" width=\"582\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-57.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-57-300x152.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 58.<br \/>\nf(x) = -x &#8211; 4 ; g(x) = x &#8211; 4<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nf (x) = -x &#8211; 4<br \/>\ng (x) = x &#8211; 4<br \/>\nHence,<br \/>\nThe representations of f (x) and g (x) in the coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-94.png\" alt=\"\" width=\"491\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-94.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-94-294x300.png 294w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and g (x) are perpendicular lines since only the slopes vary and the y-intercepts are the same<\/p>\n<p>Question 59.<br \/>\nf(x) = x + 2; g(x) = \\(\\frac{2}{3}\\)x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 59\" width=\"564\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-59.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-59-300x164.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 60.<br \/>\nf(x) = x &#8211; 1; g(x) = 3x &#8211; 3<br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nf (x) = x &#8211; 1<br \/>\ng (x) = 3x &#8211; 3<br \/>\nSo,<br \/>\ng (x) = 3 (x &#8211; 1)<br \/>\ng (x) = 3 f (x)<br \/>\nHence,<br \/>\nThe representations of f (x) and g (x) in the coordinate plane are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-95.png\" alt=\"\" width=\"484\" height=\"488\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-95.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-95-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-95-150x150.png 150w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates 3 units away from f (x)<\/p>\n<p>Question 61.<br \/>\n<b>REASONING<\/b><br \/>\nThe graph of f(x) = x + 5 is a vertical translation 5 units up of the graph of f(x) = x. How can you obtain the graph of f(x) = x + 5 from the graph of f(x) = x using a horizontal translation?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 61\" width=\"588\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-61.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-61-300x194.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Match each function with its graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-169.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 169\" width=\"212\" height=\"189\" \/><br \/>\na. a(x) = f(-x)<br \/>\nb. g(x) = f(x) &#8211; 4<br \/>\nc. h(x) = f(x) + 2<br \/>\nd. k(x) = f(3x)<br \/>\nAnswer:<\/p>\n<p><b>REASONING<br \/>\nIn Exercises 63\u201366, find the value of r.<\/b><\/p>\n<p>Question 63.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-170.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 170\" width=\"143\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 63\" width=\"570\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-63.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-63-300x59.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 64.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-171.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 171\" width=\"144\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nf (x) = -3x + 5<br \/>\ng (x) = f (rx)<br \/>\nSo,<br \/>\ng (x) = -3 (rx) + 5<br \/>\nWhere,<br \/>\nr is the transformational factor<br \/>\nFrom the graph,<br \/>\nThe x-intercept of g(x) is: 5<br \/>\nNow,<br \/>\nTo find he x-intercept, put y = 0<br \/>\nSo,<br \/>\n0 = -3 (rx) + 5<br \/>\n3 (rx) = 5<br \/>\n3r (5) = 5<br \/>\n3r = 5 \/ 5<br \/>\n3r = 1<br \/>\nr = \\(\\frac{1}{3}\\)<br \/>\nHence, from the above,<br \/>\nWE can conclude that the value of r is: \\(\\frac{1}{3}\\)<\/p>\n<p>Question 65.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-172.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 172\" width=\"138\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 65\" width=\"589\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-65.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-65-300x61.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 66.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-173.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 173\" width=\"164\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nThe given equations are:<br \/>\nf (x) = \\(\\frac{1}{2}\\)x + 8<br \/>\ng (x) = f (x) + r<br \/>\nSo,<br \/>\ng (x) = \\(\\frac{1}{2}\\)x + 8 + r<br \/>\nFrom the graph,<br \/>\nWe can observe that f (x) and g (x) are both the parallel lines<br \/>\nSo,<br \/>\nThe slopes of f (x) and g (x) are the same and only the y-intercepts differ in f (x) and g (x)<br \/>\nFrom the graph,<br \/>\nWe can observe that the y-intercept of g (x) is: 0<br \/>\nSo,<br \/>\ng (x) = \\(\\frac{1}{2}\\)x + 8 + 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of r is: 0<\/p>\n<p>Question 67.<br \/>\n<b>CRITICAL THINKING<\/b><br \/>\nWhen is the graph of y = f(x) + w the same as the graph of y = f(x + w) for linear functions? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 67\" width=\"579\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-67.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-67-300x73.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the formula for the indicated variable.<\/b>(Section 1.5)<\/p>\n<p>Question 68.<br \/>\nSolve for h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-174.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 174\" width=\"120\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nThe given formula from the given figure is:<br \/>\nV = \u03c0r\u00b2h<br \/>\nDivide by \u03c0r\u00b2 into both sides<br \/>\nSo,<br \/>\n\\(\\frac{V}{\u03c0r\u00b2}\\) = h<br \/>\nHence, from the above,<br \/>\nWe can conclude that the formula for &#8216;h&#8217; is:<br \/>\nh = \\(\\frac{V}{\u03c0r\u00b2}\\)<\/p>\n<p>Question 69.<br \/>\nSolve for w.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-175.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 175\" width=\"208\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 69\" width=\"255\" height=\"278\" \/><\/p>\n<p><b>Solve the inequality. Graph the solution, if possible.<\/b> (Section 2.6)<\/p>\n<p>Question 70.<br \/>\n| x &#8211; 3 | \u2264 14<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n| x + 3 | \u2264 14<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 3 \u2264 14 and x + 3 \u2265 -14<br \/>\nx \u2264 14 &#8211; 3 and x \u2265 -14 &#8211; 3<br \/>\nx \u2264 11 and x \u2265 -17<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions to the given absolute value inequality are:<br \/>\nx \u226411 and x \u2265 -17<br \/>\nThe representation of the solutions of the given inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-91.png\" alt=\"\" width=\"575\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-91.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-91-300x74.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 71.<br \/>\n| 2x + 4 | &gt; 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-71.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 71\" width=\"375\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-71.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-71-300x245.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<p>Question 72.<br \/>\n5 | x + 7 | &lt; 25<br \/>\nAnswer:<br \/>\nThe given absolute value inequality is:<br \/>\n5 | x + 7 | &lt; 25<br \/>\nSo,<br \/>\n| x + 7 | &lt; 25 \/ 5<br \/>\n| x + 7 | &lt; 5<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\nx + 7 &lt; 5 and x + 7 &gt; -5<br \/>\nx &lt; 5 &#8211; 7 and x &gt; -5 &#8211; 7<br \/>\nx &lt; -2 and x &gt; -12<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solutions of the given absolute value inequality are:<br \/>\nx &lt; -2 and x &gt; -12<br \/>\nThe representations of the solutions of the given absolute value inequality in the graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-63266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-92.png\" alt=\"\" width=\"567\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-92.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-92-300x76.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 73.<br \/>\n-2 | x + 1 | \u2265 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-73.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.6 Question 73\" width=\"503\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-73.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.6-Question-73-300x117.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<h3><a id=\"Lesson_3.7_Graphing_Absolute_Value_Functions\"><\/a>Lesson 3.7 Graphing Absolute Value Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow do the values of a, h, and k affect the graph of the absolute value function g(x) = a | x &#8211; h | + k? The parent absolute value function is f(x) = | x | Parent absolute value function<br \/>\nThe graph of f is V-shaped.<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\ng (x) = a | x &#8211; h | + k<br \/>\nThe parent function for the given absolute value function is:<br \/>\nf (x) = | x |<br \/>\nIt is also given that the graph of f is v-shaped<br \/>\nNow,<br \/>\nThe given absolute value function has the constants a, x, h, and k<br \/>\nNow,<br \/>\n&#8220;x &#8211; h&#8221; represents the translation of the x-axis where h is the translation value<br \/>\nEx:<br \/>\nx &#8211; h =x &#8211; 3<br \/>\nWhere,<br \/>\nx is the original function and h is the translation factor of x<br \/>\nNow,<br \/>\n&#8220;k&#8221; represents the y-intercept of the given absolute value function<br \/>\nThe value of k affects the graph of the given absolute value function to translate on the y-axis up and down or shrink and stretch<\/p>\n<p><b>EXPLORATION 1<br \/>\nIdentifying Graphs of Absolute Value Functions<br \/>\nWork with a partner.<\/b> Match each absolute value function with its graph. Then use a graphing calculator to verify your answers.<br \/>\na. g(x) = | x &#8211; 2 |<br \/>\nb. g(x) = | x &#8211; 2 | + 2<br \/>\nc. g(x) = | x + 2 | + 2<br \/>\nd. g(x) = &#8211; | x + 2 | + 2<br \/>\ne. g(x) = 2 | x &#8211; 2 |<br \/>\nf. g(x) = &#8211; | x + 2 | + 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-176.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 176\" width=\"471\" height=\"397\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-176.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-176-300x253.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\na. g(x) = | x &#8211; 2 |<br \/>\nb. g(x) = | x &#8211; 2 | + 2<br \/>\nc. g(x) = | x + 2 | + 2<br \/>\nd. g(x) = &#8211; | x + 2 | + 2<br \/>\ne. g(x) = 2 | x &#8211; 2 |<br \/>\nf. g(x) = &#8211; | x + 2 | + 2<br \/>\nWe know that,<br \/>\n| x | =x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nNow,<br \/>\na.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = | x &#8211; 2 |<br \/>\nSo,<br \/>\ng (x) = x &#8211; 2 or g (x) = &#8211; (x &#8211; 2)<br \/>\ng (x) = x &#8211; 2 or g (x) = 2 &#8211; x<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-121.png\" alt=\"\" width=\"488\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-121.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-121-300x289.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, fro the above,<br \/>\nWe can conclude that graph F) matches the given absolute value function<br \/>\nb.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = | x &#8211; 2 | + 2<br \/>\nSo,<br \/>\ng (x) = x &#8211; 2 + 2 or g (x) = &#8211; (x &#8211; 2) + 2<br \/>\ng (x) = x or g (x) = 2 &#8211; x + 2<br \/>\ng (x) = x or g (x) = 4 &#8211; x<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-122.png\" alt=\"\" width=\"484\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-122.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-122-300x295.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph C) matches the given absolute value function<br \/>\nc.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = | x + 2 | + 2<br \/>\nSo,<br \/>\ng (x) = x + 2 + 2 or g (x) = &#8211; (x + 2 ) + 2<br \/>\ng (x) = x + 4 or\u00a0 g (x) = -x &#8211; 2 + 2<br \/>\ng (x) = x + 4 or g (x) = -x<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-123.png\" alt=\"\" width=\"485\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-123.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-123-300x295.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph C) matches the given absolute value function<br \/>\nd.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = &#8211; | x + 2 | + 2<br \/>\nSo,<br \/>\ng (x) = &#8211; (x + 2 )\u00a0 + 2 or g (x) = &#8211; [- (x + 2 ) ] + 2<br \/>\ng (x) = -x &#8211; 2 + 2 or g (x) = x + 2 + 2<br \/>\ng (x) = x or g (x) =x + 4<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-124.png\" alt=\"\" width=\"480\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-124.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-124-300x296.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph B) matches the given absolute value function<br \/>\ne.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = 2 | x &#8211; 2 |<br \/>\nSo,<br \/>\ng (x) = 2 (x &#8211; 2) or g (x) = 2 ( &#8211; (x &#8211; 2) )<br \/>\ng (x) = 2x &#8211; 4 or g (x) = 2 (-x + 2 )<br \/>\ng (x)= 2x &#8211; 4 or g (x) = -2x + 4<br \/>\nHence,<br \/>\nThe representation of the given absolue value functions in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-125.png\" alt=\"\" width=\"481\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-125.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-125-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-125-150x150.png 150w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the graph A) matches the given absolute value function<br \/>\nf.<br \/>\nThe given absolute value function is:<br \/>\ng(x) = &#8211; | x + 2 | + 2<br \/>\nSo,<br \/>\ng (x) = &#8211; (x + 2) + 2 or g (x) = &#8211; [- (x &#8211; 2} ] + 7<br \/>\ng (x) = x + 4 or g (x) = 2 &#8211; x + 7<br \/>\ng (x) = x + 4 or g (x) = -x + 9<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-126.png\" alt=\"\" width=\"483\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-126.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-126-300x288.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that graph E) matches the given absolute value function<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow do the values of a, h, and k affect the graph of the absolute value function g(x) = a | x &#8211; h | + k?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-176.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 176.1\" width=\"218\" height=\"161\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\ng (x) = a | x &#8211; h | + k<br \/>\nFrom the above absolute value function,<br \/>\nWe can say that<br \/>\na, h and k are constants<br \/>\nNow,<br \/>\n&#8220;a&#8221; represents the constant to multiply g (x)<br \/>\n&#8220;h&#8221; represents the translation factor on the x-axis<br \/>\n&#8220;k&#8221; represents the y-intercept of the given function<br \/>\nThe value of &#8220;h&#8221; and &#8220;k&#8221; affect the graph in such a way that the graph can move anywhere in the graph<\/p>\n<p>Question 3.<br \/>\nWrite the equation of the absolute value function whose graph is shown. Use a graphing calculator to verify your equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-177.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 177\" width=\"177\" height=\"130\" \/><br \/>\nAnswer:<br \/>\nThe given graphing calculator is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-177.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 177\" width=\"177\" height=\"130\" \/><br \/>\nFrom the above graph,<br \/>\nWe can observe that the plot is in downwqrd direction i.e., the absolute value fuction is negative and the plot passes through 2 in the x-axis<br \/>\nHence,<br \/>\nThe absolute value function representing the given graph is:<br \/>\nf (x) = -| x + 1 | + 2<\/p>\n<p><b>3.7 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range.<\/b><\/p>\n<p>Question 1.<br \/>\nh(x) = | x | &#8211; 1<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nh (x) = | x | &#8211; 1<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in\u00a0 the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-127.png\" alt=\"\" width=\"495\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-127.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-127-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-127-150x150.png 150w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nHence, from the above graph,<br \/>\nh (x) is translated vertically away from f (x) on the y-axis by 1unit<br \/>\nNow,<br \/>\nThe domain of the given functions are: -10 \u2264 x \u2264 10<br \/>\nThe range of the given functions are: -1 \u2264 y \u2264 10<\/p>\n<p>Question 2.<br \/>\nn(x) = | x + 4 |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nh (x) = | x + 4 |<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-128.png\" alt=\"\" width=\"485\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-128.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-128-293x300.png 293w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above graph,<br \/>\nh (x) is translated from f (x) 4 units away on the x-axis<br \/>\nNow,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of h (x) is: -10 \u2264 x \u22646<br \/>\nThe range of f (x) is: 0 \u2264 y \u2264 10<br \/>\nThe range of h (x) is: 0 \u2264y \u2264 6<\/p>\n<p><b>Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range.<\/b><\/p>\n<p>Question 3.<br \/>\nt(x) = -3| x |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nt (x) = -3 | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and t (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-129.png\" alt=\"\" width=\"484\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-129.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-129-289x300.png 289w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above graph,<br \/>\nt (x) is shrunk by 3units and rotated by 90\u00b0 on the y-axis<br \/>\nNow,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of t (x) is: -3 \u2264x \u2264 3<br \/>\nThe range of f (x) is: 0 \u2264 y \u2264 10<br \/>\nThe range of t (x) is: -10 \u2264 y \u2264 0<\/p>\n<p>Question 4.<br \/>\nv(x) = \\(\\frac{1}{4}\\)| x |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nv (x) = \\(\\frac{1}{4}\\)| | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and v (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-130.png\" alt=\"\" width=\"495\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-130.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-130-285x300.png 285w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nHence, from the above graph,<br \/>\nt (x) translates \\(\\frac{1}{4}\\)| units of f (x) on the y-axis<br \/>\nNow,<br \/>\nThe domain of the given functions are: -10 \u2264 x \u2264 10<br \/>\nThe range of f (x) is: 0 \u2264 y \u2264 10<br \/>\nThe range of t (x) is: 0 \u2264 y \u2264 2.5<\/p>\n<p>Question 5.<br \/>\nGraph f(x) = | x &#8211; 1 | and g(x) = | \\(\\frac{1}{2}\\)x &#8211; 1 |.<br \/>\nCompare the graph of g to the graph of f.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x &#8211; 1 |<br \/>\ng (x) = | \\(\\frac{1}{2}\\)x &#8211; 1 |<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-131.png\" alt=\"\" width=\"506\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-131.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-131-291x300.png 291w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\nHence, from the above graph,<br \/>\ng (x) translates 1 unit away from f (x) on the x-axis<br \/>\nNow,<br \/>\nThe domain of f (x) is: -8 \u2264 x \u2264\u00a0 10<br \/>\nThe domain of g (x) is: -10 \u2264\u00a0 x \u2264\u00a0 10<br \/>\nThe range of f (x) is: 0 \u2264\u00a0 y \u2264 10<br \/>\nThe range of g (x) is: 0 \u2264\u00a0 y \u2264\u00a0 6<\/p>\n<p>Question 6.<br \/>\nGraph f(x) = | x + 2 | + 2 and g(x) = | -4x + 2 | + 2.<br \/>\nCompare the graph of g to the graph of f.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x + 2 | + 2<br \/>\ng (x) = | -4x + 2 | + 2<br \/>\nHence,<br \/>\nThe representation of f (x) and g(x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64533\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-132.png\" alt=\"\" width=\"481\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-132.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-132-289x300.png 289w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nHence, from the above graph,<br \/>\ng (x) translates \\(\\frac{3}{2}\\) units away from f (x) on the x-axis<br \/>\nNow,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264\u00a06<br \/>\nThe domain of g (x) is:-1.5 \u2264 x \u2264 2.5<br \/>\nThe range of f (x) is: 0 \u2264 y \u2264 10<br \/>\nThe range of g (x) is: 2 \u2264y \u2264 10<\/p>\n<p>Question 7.<br \/>\nLet g(x) = | &#8211;\\(\\frac{1}{2}\\)x + 2 | + 1.<br \/>\n(a) Describe the transformations from the graph of f(x) = | x | to the graph of g.<br \/>\n(b) Graph g.<br \/>\nAnswer:<br \/>\na.<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\ng (x) = | &#8211;\\(\\frac{1}{2}\\)x + 2 | + 1<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-133.png\" alt=\"\" width=\"500\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-133.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-133-292x300.png 292w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nHence, from the above graph,<br \/>\nWe can observe that<br \/>\ng (x) translates 4 units away from f (x) on the positive x-axis<br \/>\ng (x) translates 2 units away from f (x) on the negative x-axis<\/p>\n<p>b.<br \/>\nThe function of g (x) is:<br \/>\n| &#8211;\\(\\frac{1}{2}\\)x + 2 | + 1<br \/>\nWe know that,<br \/>\ng can be written as g (x)<br \/>\nHence,<br \/>\nThe representation of g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-134.png\" alt=\"\" width=\"504\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-134.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-134-300x280.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<h3><a id=\"Graphing_Absolute_Value_Functions_3.7_Exercises\"><\/a>Graphing Absolute Value Functions 3.7 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b><br \/>\nThe point (1, -4) is the _______ of the graph of f(x) = -3 | x &#8211; 1 | &#8211; 4.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 1\" width=\"432\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-1.png 432w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-1-300x42.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nHow do you know whether the graph of f(x) = a | x &#8211; h | + k is a vertical stretch or a vertical shrink of the graph of f(x) = | x | ?<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf (x) = a | x &#8211; h | + k<br \/>\nWhere,<br \/>\na is the vertical stretch or vertical shrink<br \/>\nh is the horizontal translation<br \/>\nk is the vertical shift<br \/>\nNow,<br \/>\n&#8216;a&#8217; will be the vertical stretch if the value of a is an integer<br \/>\n&#8216;a&#8217; will be the vertical shrink if the value of &#8216;a&#8217; is a fraction<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given function is a vertical stretch<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b><br \/>\nDescribe three different types of transformations of the graph of an absolute value function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 3\" width=\"568\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-3.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-3-300x174.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>REASONING<\/b><br \/>\nThe graph of which function has the same y-intercept as the graph of f(x) = | x &#8211; 2 | + 5? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-178.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 178\" width=\"317\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-178.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-178-300x43.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\na. f (x) = | x &#8211; 2 | + 5<br \/>\nb. g (x) = | 3x &#8211; 2 | + 5<br \/>\nc. h (x) = 3 | x &#8211; 2 | + 5<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nNow,<br \/>\na.<br \/>\nThe given absolute value function is:<br \/>\nf (x) = | x &#8211; 2 | + 5<br \/>\nSo,<br \/>\nf (x) = x &#8211; 2 + 5 or f (x) = -(x &#8211; 2) + 5<br \/>\nf (x) = x + 3 or f (x) = -x + 2 + 5<br \/>\nf (x) = x + 3 or f (x) = -x + 7<\/p>\n<p>b.<br \/>\nThe given absolute value function is:<br \/>\ng (x) = | 3x &#8211; 2 | + 5<br \/>\nSo,<br \/>\ng (x) = 3x &#8211; 2 + 5 or g (x) = &#8211; (3x &#8211; 2 ) + 5<br \/>\ng (x) = 3x + 3 or g (x) = -3x + 2 + 5<br \/>\ng (x) = 3x + 3 or g (x) = -3x + 7<\/p>\n<p>c.<br \/>\nThe given absolute value function is:<br \/>\nh (x) = 3 | x &#8211; 2 | + 5<br \/>\nSo,<br \/>\nh (x) = 3 (x &#8211; 2) + 5 or h (x) = -3 (x &#8211; 2) + 5<br \/>\nh (x) = 3x &#8211; 6 + 5 or h (x) = -3x + 6 + 5<br \/>\nh (x) = 3x &#8211; 1 or h (x) = -3x + 11<br \/>\nCompare the solutions of the given absolute value functions with<br \/>\nf (x) = mx + c<br \/>\nWhere,<br \/>\nm is the slope<br \/>\nc is the y-intercept<br \/>\nHence, from the above,<br \/>\nWe can conclude that a) and b ) have the same y-intercepts<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201312, graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range.<\/b><\/p>\n<p>Question 5.<br \/>\nd(x) = | x | &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 5\" width=\"571\" height=\"435\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-5.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-5-300x229.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 6.<br \/>\nr(x) = | x | + 5<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nr (x) = | x | + 5<br \/>\nHence,<br \/>\nThe representation of f (x) and r (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-155.png\" alt=\"\" width=\"488\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-155.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-155-295x300.png 295w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that r (x) is 5 units away from f (x)<br \/>\nNow,<br \/>\nThe domain of the given absolute value function is: -5 \u2264 x \u2264 5<br \/>\nThe range of the given absolute value function is: 5 \u2264y \u226410<\/p>\n<p>Question 7.<br \/>\nm(x) = | x + 1 |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 7\" width=\"572\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-7.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-7-300x225.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 8.<br \/>\nv(x) = | x &#8211; 3 |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nv (x) = | x &#8211; 3 |<br \/>\nHence,<br \/>\nThe representation of f(x) and v (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-156.png\" alt=\"\" width=\"487\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-156.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-156-290x300.png 290w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that v (x) translates 3 units away from f (x)<br \/>\nNow,<br \/>\nThe domain of the given absolute value function is: -6 \u2264 x \u2264 10<br \/>\nThe range of the given absolute value function is: 6 \u2264 y \u2264 10<\/p>\n<p>Question 9.<br \/>\np(x) = \\(\\frac{1}{3}\\) | x |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 9\" width=\"585\" height=\"463\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-9.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-9-300x237.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 10.<br \/>\nj(x) = 3 | x |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nj (x) = 3 | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and j (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-157.png\" alt=\"\" width=\"482\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-157.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-157-288x300.png 288w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that j (x) vertically stretches 3 units away from f (x)<br \/>\nNow,<br \/>\nThe domain of the given absolute value function is: -3.5 \u2264 x \u2264 3.5<br \/>\nThe range of the given absolute value function is: 0 \u2264 y \u2264 10<\/p>\n<p>Question 11.<br \/>\na(x) = -5 | x |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 11\" width=\"580\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-11.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-11-300x240.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 12.<br \/>\nq(x) = &#8211; \\(\\frac{3}{2}\\) | x |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nq (x) = &#8211;\\(\\frac{3}{2}\\) | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and q (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-159.png\" alt=\"\" width=\"497\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-159.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-159-285x300.png 285w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that q (x) shrinks by \\(\\frac{3}{2}\\) units from f (x)<br \/>\nNow,<br \/>\nThe domain of the given absolute value function is: -6.5 \u2264 x \u2264 6.5<br \/>\nThe range of the given absolute value function is: -10 \u2264 y \u2264 0<\/p>\n<p><b>In Exercises 13\u201316, graph the function. Compare the graph to the graph of f(x) = | x \u2212 6 |.<\/b><\/p>\n<p>Question 13.<br \/>\nh(x) = | x &#8211; 6 | + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 13\" width=\"558\" height=\"430\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-13.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-13-300x231.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 14.<br \/>\nn(x) = \\(\\frac{1}{2}\\) | x &#8211; 6 |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x &#8211; 6 |<br \/>\nn (x) = \\(\\frac{1}{2}\\) | x &#8211; 6 |<br \/>\nHence,<br \/>\nThe representation of f (x) and n (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-153.png\" alt=\"\" width=\"508\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-153.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-153-293x300.png 293w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that n (x) vertically stretches \\(\\frac{1}{2}\\) units of f (x)<\/p>\n<p>Question 15.<br \/>\nk(x) = -3 | x &#8211; 6 |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 15\" width=\"557\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-15.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-15-300x228.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 16.<br \/>\ng(x) = | x &#8211; 1 |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x &#8211; 6 |<br \/>\ng (x) = | x &#8211; 1 |<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-154.png\" alt=\"\" width=\"484\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-154.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-154-288x300.png 288w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates 4 units away from f (x) on the positive x-axis<\/p>\n<p><b>In Exercises 17 and 18, graph the function. Compare the graph to the graph of f(x) = | x + 3 | \u2212 2.<\/b><\/p>\n<p>Question 17.<br \/>\ny(x) = | x + 4 | &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 17\" width=\"585\" height=\"427\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-17.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-17-300x219.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 18.<br \/>\nb(x) = | x + 3 | + 3<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x + 3 | &#8211; 2<br \/>\nb (x) = | x + 3 | + 3<br \/>\nHence,<br \/>\nThe representation of f (x) and b (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-152.png\" alt=\"\" width=\"494\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-152.png 494w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-152-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-152-150x150.png 150w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and b (x) are parallel lines since the slopes are constant and there are different values of the y-intercepts<\/p>\n<p><b>In Exercises 19\u201322, compare the graphs. Find the value of h, k, or a.<\/b><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-179.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 179\" width=\"171\" height=\"161\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 19\" width=\"535\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-19.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-19-300x33.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-180.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 180\" width=\"160\" height=\"162\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-180.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 180\" width=\"160\" height=\"162\" \/><br \/>\nFrom the above graph,<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\nt (x) = | x &#8211; h |<br \/>\nWhere,<br \/>\nh is the horizontal translation<br \/>\nFrom the graph,<br \/>\nWe can observe that the translation occurs at (1, 0) of f (x)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of &#8216;h&#8217; is: 1<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-3-Graphing-Linear-Functions-181.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 3 Graphing Linear Functions 181\" width=\"156\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 21\" width=\"575\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-21.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-21-300x32.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-182.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 182\" width=\"154\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-182.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 182\" width=\"154\" height=\"157\" \/><br \/>\nFrom the given graph,<br \/>\nThe given graphs are:<br \/>\nf (x) = | x |<br \/>\nw (x) = a | x |<br \/>\nWhere,<br \/>\n&#8216;a&#8217; is the vertical stretch<br \/>\nFrom the graph,<br \/>\nWe can observe that the vertical stretch occurs at (0, 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of a is: 2<\/p>\n<p><b>In Exercises 23\u201326, write an equation that represents the given transformation(s) of the graph of g(x) = | x |.<\/b><\/p>\n<p>Question 23.<br \/>\nvertical translation 7 units down<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 23\" width=\"552\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-23.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-23-300x63.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 24.<br \/>\nhorizontal translation 10 units left<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nHorizontal translation 10 units left<br \/>\nLet the absolute value function be y = | x |<br \/>\nSo,<br \/>\n&#8220;Horizontal translation&#8221; means the moving of value on the x-axis either to the left side or the right side i.e., either on the negative or positive x-axis<br \/>\nSo,<br \/>\nThe given statement in the absolute value function form is:<br \/>\ny = | x | + 10<\/p>\n<p>Question 25.<br \/>\nvertical shrink by a factor of \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 25\" width=\"557\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-25.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-25-300x50.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 26.<br \/>\nvertical stretch by a factor of 3 and a reflection in the x-axis<br \/>\nAnswer:<br \/>\nThe given statement is:<br \/>\nVertical stretch by a factor of 3 and a reflection in the x-axis<br \/>\nWe know that,<br \/>\nThe representation of the vertical stretch &#8216;a&#8217; of the function is:<br \/>\ny = a.f (x)<br \/>\nThe representation of the reflection of the function is:<br \/>\ny= f (-x)<br \/>\nNow,<br \/>\nLet the absolute value function be<br \/>\ny = x<br \/>\nHence,<br \/>\nThe representation of the given statement in the absolute value function form is:<br \/>\nVertical stretch:<br \/>\ny = 3x<br \/>\nReflection:<br \/>\ny = -3x<\/p>\n<p><b>In Exercises 27\u201332, graph and compare the two functions.<\/b><\/p>\n<p>Question 27.<br \/>\nf(x) = | x &#8211; 4 |; g(x) = | 3x &#8211; 4 |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 27\" width=\"584\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-27.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-27-300x274.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 28.<br \/>\nh(x) = | x + 5 |; t(x) = | 2x + 5 |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nh (x) = | x + 5 |<br \/>\nt (x) = | 2x + 5 |<br \/>\nHence,<br \/>\nThe representation of h (x) and t (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-146.png\" alt=\"\" width=\"493\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-146.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-146-295x300.png 295w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that t (x) translates 6 units away from h (x) in the negative y-axis<\/p>\n<p>Question 29.<br \/>\np(x) = | x + 1 | &#8211; 2; q(x) = | \\(\\frac{1}{4}\\)x + 1 | &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 29\" width=\"570\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-29.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-29-300x276.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 30.<br \/>\nw(x) = | x &#8211; 3 | + 4; y(x) = | 5x &#8211; 3 | + 4<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nw (x) = | x &#8211; 3 | + 4<br \/>\ny (x) = | 5x &#8211; 3 | + 4<br \/>\nHence,<br \/>\nThe representation of w (x) and y (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-148.png\" alt=\"\" width=\"488\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-148.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-148-292x300.png 292w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that w (x) is 7 units away from y (x) in the positive y-axis<\/p>\n<p>Question 31.<br \/>\na(x) = | x + 2 | + 3; b(x) = | -4x + 2 | + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 31\" width=\"554\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-31.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-31-300x292.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 32.<br \/>\nu(x) = | x &#8211; 1 | + 2; v(x) = | &#8211;\\(\\frac{1}{2}\\)x &#8211; 1 | + 2<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nu (x) = | x &#8211; 1 | + 2<br \/>\nv (x) = | &#8211;\\(\\frac{1}{2}\\)x &#8211; 1 | + 2<br \/>\nHence,<br \/>\nThe representation of u (x) and v (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-151.png\" alt=\"\" width=\"583\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-151.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-151-300x270.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that u (x) is 1 unit away from v (x) in the positive y-axis<\/p>\n<p><b>In Exercises 33\u201340, describe the transformations from the graph of f(x) = | x | to the graph of the given function. Then graph the given function.<\/b><\/p>\n<p>Question 33.<br \/>\nr(x) = | x + 2 | &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 33\" width=\"566\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-33.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-33-300x161.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 34.<br \/>\nc(x) = | x + 4 | + 4<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\nc (x) = | x + 4 | + 4<br \/>\nHence,<br \/>\nThe representation of c (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-142.png\" alt=\"\" width=\"477\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-142.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-142-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-142-150x150.png 150w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that c (x) translates 4 units away in the positive x-axis and 4 units vertically in the y-axis<\/p>\n<p>Question 35.<br \/>\nd(x) = &#8211; | x &#8211; 3 | + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 35\" width=\"574\" height=\"301\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-35.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-35-300x157.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 36.<br \/>\nv(x) = -3| x + 1 | + 4<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\nv (x) = -3 | x + 1 | + 4<br \/>\nHence,<br \/>\nThe representation of v (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-143.png\" alt=\"\" width=\"481\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-143.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-143-300x296.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that v (x) translates 4 units vertically above and 2 units to the right side of the positive x-axis<\/p>\n<p>Question 37.<br \/>\nm(x) = \\(\\frac{1}{2}\\) | x + 4 | &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 37\" width=\"576\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-37.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-37-300x158.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 38.<br \/>\ns(x) = | 2x &#8211; 2 | &#8211; 3<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\ns (x) = | 2x &#8211; 2 | &#8211; 3<br \/>\nHence,<br \/>\nThe representation of s (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-144.png\" alt=\"\" width=\"482\" height=\"479\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-144.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-144-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-144-150x150.png 150w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that s (x) translates 4 units away to the right side of the positive x-axis<\/p>\n<p>Question 39.<br \/>\nj(x) = | -x + 1 | &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 39\" width=\"556\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-39.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-39-300x163.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 40.<br \/>\nn(x) = | &#8211;\\(\\frac{1}{3}\\)x + 1 | + 2<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\nn (x) = | &#8211;\\(\\frac{1}{3}\\)x + 1 | + 2<br \/>\nHence,<br \/>\nThe representation of n (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-145.png\" alt=\"\" width=\"477\" height=\"466\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-145.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-145-300x293.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that n (x) translates 4 units away from the origin<\/p>\n<p>Question 41.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe number of pairs of shoes sold s (in thousands) increases and then decreases as described by the function s(t) = -2 | t &#8211; 15 | + 50, where t is the time (in weeks).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-183.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 183\" width=\"245\" height=\"124\" \/><br \/>\na. Graph the function.<br \/>\nb. What is the greatest number of pairs of shoes sold in 1 week?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 41\" width=\"581\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-41.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-41-300x242.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nOn the pool table shown, you bank the five ball off the side represented by the x-axis. The path of the ball is described by the function p(x) = \\(\\frac{4}{3}\\) | x &#8211; \\(\\frac{5}{4}\\) |.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-184.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 184\" width=\"240\" height=\"145\" \/><br \/>\na. At what point does the five-ball bank off the side?<br \/>\nAnswer:<br \/>\nIt is given that on the pool table shown, you bank the five ball off the side represented by the x-axis. The path of the ball is described by the function<br \/>\np(x) = \\(\\frac{4}{3}\\) | x &#8211; \\(\\frac{5}{4}\\) |<br \/>\nNow,<br \/>\nTo find the point where the five-ball bank off the side, draw the plot of the given absolute value function<br \/>\nSo,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-141.png\" alt=\"\" width=\"490\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-141.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-141-272x300.png 272w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nHence, from the above,<br \/>\nThe point where the five-ball offside is: (1, 0)<\/p>\n<p>b. Do you make the shot? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-184.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 184\" width=\"240\" height=\"145\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the point is accurately going through the hole i.e., at (5, 5)<br \/>\nHence, from the above,<br \/>\nWe can conclude that you make the shot<\/p>\n<p>Question 43.<br \/>\n<b>USING TRANSFORMATIONS<\/b><br \/>\nThe points A (-\\(\\frac{1}{2}\\), 3) , B(1, 0), and C(-4, -2) lie on the graph of the absolute value function f. Find the coordinates of the points corresponding to A, B, and C on the graph of each function.<br \/>\na. g(x) = f(x) &#8211; 5<br \/>\nb. h(x) = f(x &#8211; 3)<br \/>\nc. j(x) = -f(x)<br \/>\nd. k(x) = 4f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 43.1\" width=\"894\" height=\"554\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.1.png 894w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.1-300x186.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.1-768x476.png 768w\" sizes=\"(max-width: 894px) 100vw, 894px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 43.2\" width=\"872\" height=\"606\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.2.png 872w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.2-300x208.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.2-768x534.png 768w\" sizes=\"(max-width: 872px) 100vw, 872px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 43.3\" width=\"843\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.3.png 843w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.3-300x45.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-43.3-768x115.png 768w\" sizes=\"(max-width: 843px) 100vw, 843px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nExplain how the graph of each function compares to the graph of y = | x | for positive and negative values of k, h, and a.<br \/>\na.y = | x | + k<br \/>\nb. y = | x &#8211; h |<br \/>\nc. y = a| x |<br \/>\nd. y = | ax |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\na.y = | x | + k<br \/>\nb. y = | x &#8211; h |<br \/>\nc. y = a| x |<br \/>\nd. y = | ax |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nIt is given that<br \/>\nThe parent function is:<br \/>\ny = | x |<br \/>\nNow,<br \/>\na.<br \/>\nThe given absolute value function is:<br \/>\ny = | x | + k<br \/>\nHence,<br \/>\nThe given absolute value function translates from the parent function k units away in the positive y-axis vertically<br \/>\nb.<br \/>\nThe given absolute value function is:<br \/>\ny = | x &#8211; h |<br \/>\nHence,<br \/>\nThe given absolute value function translates from the parent function h units away in the positive x-axis horizontally<br \/>\nc.<br \/>\nThe given absolute value function is:<br \/>\ny = a| x |<br \/>\nHence,<br \/>\nThe given absolute value function reflects from the parent function &#8216;a&#8217; units away<br \/>\nd.<br \/>\nThe given absolute value function is:<br \/>\ny = | ax |<br \/>\nHence,<br \/>\nThe given absolute value function dilates from the parent function with the value of &#8216;a&#8217; units<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 45 and 46, describe and correct the error in graphing the function.<\/b><\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-185.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 185\" width=\"332\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-185.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-185-300x136.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 45\" width=\"579\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-45.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-45-300x184.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-186.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 186\" width=\"332\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-186.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-186-300x140.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\ny = -3 | x|<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ny = -3 (x) or y = -3 (-x)<br \/>\nSo,<br \/>\ny = -3x or y = 3x<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-140.png\" alt=\"\" width=\"493\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-140.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-140-296x300.png 296w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the given absolute value function in downward direction<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 47 and 48, write an absolute value function whose graph forms a square with the given graph.<\/b><\/p>\n<p>Question 47.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-187.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 187\" width=\"174\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 47\" width=\"586\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-47.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-47-300x118.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-188.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 188\" width=\"171\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-188.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 188\" width=\"171\" height=\"140\" \/><br \/>\nFrom the graph,<br \/>\nThe given absolute value function is:<br \/>\ny = | x &#8211; 3 | + 1<br \/>\nFrom the given absolute value function,<br \/>\nWe can say that the x-axis translates 3 units away in the positive x-axis and the y-axis is a vertical stretch with the value of k as 1<\/p>\n<p>Question 49.<br \/>\n<b>WRITING<\/b><br \/>\nCompare the graphs of p(x) = | x &#8211; 6 | and q(x) = | x | &#8211; 6.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 49\" width=\"553\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-49.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-49-300x48.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> The object of a computer game is to break bricks by deflecting a ball toward them using a paddle. The graph shows the current path of the ball and the location of the last brick.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 189\" width=\"328\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189-300x192.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\na. You can move the paddle up, down, left, and right. At what coordinates should you place the paddle to break the last brick? Assume the ball deflects at a right angle.<br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 189\" width=\"328\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-189-300x192.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nIt is given that the paddle moves at the right angle using a ball<br \/>\nSo,<br \/>\nFrom the graph,<br \/>\nThe coordinates that are at a right angle to break the brick using a paddle is:<br \/>\n(3, 8) and (14, 8)<\/p>\n<p>b. You move the paddle to the coordinates in part (a), and the ball is deflected. How can you write an absolute value function that describes the path of the ball?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe coordinates that are used to break the brick using a paddle is:<br \/>\n(3, 8) and (14, 8)<br \/>\nWe know that,<br \/>\nFor absolute value function,<br \/>\nThe parent function will always be:<br \/>\nf (x) = | x |<br \/>\nFrom part (a),<br \/>\nThe y-axis is constant and the x-axis is translating 3 units away and 14 units away<br \/>\nWe know that,<br \/>\nThe value of the absolute value function with the translation of x-value and\u00a0 y-value as k-value<br \/>\nSo,<br \/>\nf (x) = | x &#8211; h | + k<br \/>\nHence,<br \/>\nThe absolute value function that describes the path of the ball is:<br \/>\nf (x) = | x &#8211; 3 | + 8<br \/>\nf (x) = | x &#8211; 14 | + 8<\/p>\n<p><b>In Exercises 51\u201354, graph the function. Then rewrite the absolute value function as two linear functions, one that has the domain x &lt; 0 and one that has the domain x \u2265 0.<\/b><\/p>\n<p>Question 51.<br \/>\ny = | x |<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 51\" width=\"270\" height=\"279\" \/><\/p>\n<p>Question 52.<br \/>\ny = | x | &#8211; 3<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ny = x &#8211; 3 or y = -x &#8211; 3<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-138.png\" alt=\"\" width=\"505\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-138.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-138-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-138-150x150.png 150w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 53.<br \/>\ny = &#8211; | x | + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 53\" width=\"328\" height=\"430\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-53.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-53-229x300.png 229w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 54.<br \/>\ny = &#8211; 4 | x |<br \/>\nAnswer:<br \/>\nThe given absolute value function is:<br \/>\ny = -4 | x |<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ny = -4 (x) or y = -4 (-x)<br \/>\ny = -4x or y = 4x<br \/>\nHence,<br \/>\nThe representation of the given absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-139.png\" alt=\"\" width=\"497\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-139.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-139-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-139-150x150.png 150w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p><b>In Exercises 55\u201358, graph and compare the two functions<\/b>.<\/p>\n<p>Question 55.<br \/>\nf(x) = | x &#8211; 1 | + 2; g(x) = 4 | x &#8211; 1 | + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 55\" width=\"582\" height=\"512\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-55.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-55-300x264.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 56.<br \/>\ns(x) = | 2x &#8211; 5 | &#8211; 6; t(x) = \\(\\frac{1}{2}\\) | 2x &#8211; 5 | &#8211; 3<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\ns (x) = | 2x &#8211; 5 | &#8211; 6<br \/>\nt (x) = \\(\\frac{1}{2}\\) | 2x &#8211; 5 | &#8211; 3<br \/>\nHence,<br \/>\nThe representation of s (x) and t (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-136.png\" alt=\"\" width=\"497\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-136.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-136-286x300.png 286w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that s (x) translates 60 units away from t (x)<\/p>\n<p>Question 57.<br \/>\nv(x) = -2 | 3x + 1 | + 4; w(x) = 3 | 3x + 1 | &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 57\" width=\"581\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-57.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-57-271x300.png 271w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 58.<br \/>\nc(x) = 4 | x + 3 | &#8211; 1; d(x) = &#8211;\\(\\frac{4}{3}\\) | x + 3 | + \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nc (x) = 4 | x + 3 | &#8211; 1<br \/>\nd (x) =-\\(\\frac{4}{3}\\) | x + 3 | + \\(\\frac{1}{3}\\)<br \/>\nHence,<br \/>\nThe representation of c (x) and d (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-137.png\" alt=\"\" width=\"553\" height=\"532\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-137.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-137-300x289.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that d(x) and c (x) are opposite to each other<\/p>\n<p>Question 59.<br \/>\n<b>REASONING<br \/>\n<\/b>Describe the transformations from the graph of g(x) = -2 | x + 1 | + 4 to the graph of h(x) =| x |. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 59\" width=\"586\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-59.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-59-300x146.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 60.<br \/>\n<b>THOUGHT-PROVOKING<\/b><br \/>\nGraph an absolute value function f that represents the route a wide receiver runs in a football game. Let the x-axis represent the distance (in yards) across the field horizontally. Let the y-axis represent the distance (in yards) down the field. Be sure to limit the domain so the route is realistic.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nLet the x-axis represent the distance (in yards) across the field horizontally<br \/>\nLet the y-axis represent the distance (in yards) down the field.<br \/>\nLet,<br \/>\nThe distance across the field horizontally is: 50 yards<br \/>\nThe distance down the field is: 25 yards<br \/>\nRemember we can take any value in the x-axis and the y-axis<br \/>\nSo,<br \/>\n(x, y) = (50, 25)<br \/>\nSo,<br \/>\nThe absolute value function f that represents the route a wide receiver runs in a football game is:<br \/>\nf (x) = | x &#8211; 50 | + 25<br \/>\nHence,<br \/>\nThe representation of the above absolute value function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-135.png\" alt=\"\" width=\"495\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-135.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-135-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-135-150x150.png 150w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\nHence, from the above,<br \/>\nThe domain of the given absolute value function is: x \u2265 0<br \/>\nThe range of the given absolute value function is: y &gt; 0<\/p>\n<p>Question 61.<br \/>\n<b>SOLVING BY GRAPHING<\/b><br \/>\nGraph y = 2 | x + 2 | &#8211; 6 and y = -2 in the same coordinate plane. Use the graph to solve the equation 2 | x + 2 | &#8211; 6 = -2. Check your solutions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 61\" width=\"512\" height=\"583\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-61.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-61-263x300.png 263w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nLet p be a positive constant. Your friend says that because the graph of y =| x | + p is a positive vertical translation of the graph of y = | x |, the graph of y = | x + p | is a positive horizontal translation of the graph of y = | x |. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nIt is given that your friend says that because the graph of y =| x | + p is a positive vertical translation of the graph of y = | x |, the graph of y = | x + p | is a positive horizontal translation of the graph of y = | x |.<br \/>\nNow,<br \/>\nThe graph of<br \/>\ny = | x | + p is a positive vertical translation because the y-intercept in the given equation is positive<br \/>\nNow,<br \/>\nThe graph of<br \/>\ny = | x + p | will be a horizontal translation with negative translation value<br \/>\nBut, according to your friend,<br \/>\ny = | x + p | is a positive horizontal translation<br \/>\nHence, from the above,<br \/>\nWe can conclude that your friend is not correct<\/p>\n<p>Question 63.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nWrite the vertex of the absolute value function f(x) = | ax &#8211; h | + k in terms of a, h, and k.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 63\" width=\"576\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-63.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-63-300x190.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the inequality. <\/b>(Section 2.4)<\/p>\n<p>Question 64.<br \/>\n8a &#8211; 7 \u2264 2(3a &#8211; 1)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n8a &#8211; 7 \u2264 2 (3a &#8211; 1)<br \/>\nSo,<br \/>\n8a &#8211; 7 \u2264 2 (3a) &#8211; 2 (1)<br \/>\n8a &#8211; 7 \u2264 6a &#8211; 2<br \/>\n8a &#8211; 6a \u2264 -2 + 7<br \/>\n2a \u2264 5<br \/>\na \u2264 \\(\\frac{5}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the solution to the given inequality is:<br \/>\na \u2264 \\(\\frac{5}{2}\\)<\/p>\n<p>Question 65.<br \/>\n-3(2p + 4) &gt; -6p &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 65\" width=\"543\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-65.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-65-300x97.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 66.<br \/>\n4(3h + 1.5) \u2265 6(2h &#8211; 2)<br \/>\nAnswer:<br \/>\nThe given inequality is:<br \/>\n4 (3h + 1.5) \u2265 6 (2h &#8211; 2)<br \/>\nSo,<br \/>\n4 (3h) + 4 (1.5) \u2265 6 (2h) &#8211; 6 (2)<br \/>\n12h + 6 \u2265 12h &#8211; 12<br \/>\n12h &#8211; 12h + 6 \u2265 -12<br \/>\n6 \u2265 -12<br \/>\nSince the above inequality is true,<br \/>\nThe given inequality has infinite solutions<\/p>\n<p>Question 67.<br \/>\n-4(x + 6) &lt; 2(2x &#8211; 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 67\" width=\"265\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-67.png 265w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-67-210x300.png 210w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><\/p>\n<p><b>Find the slope of the line. <\/b>(Section 3.5)<\/p>\n<p>Question 68.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-190.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 190\" width=\"160\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-190.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 190\" width=\"160\" height=\"132\" \/><br \/>\nFrom the above graph,<br \/>\nThe points are: (0, 3), (-2, -2)<br \/>\nWe know that,<br \/>\nThe slope of the give line when (x1, y1), (x2, y2) are given is:<br \/>\nm= \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\n(x1, y1) = (0, 3) and (x2, y2) = (-2, -2)<br \/>\nSo,<br \/>\nm = \\(\\frac{-2 &#8211; 3}{-2 &#8211; 0}\\)<br \/>\nm = \\(\\frac{-5}{-2}\\)<br \/>\nm = \\(\\frac{5}{2}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: \\(\\frac{5}{2}\\)<\/p>\n<p>Question 69<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-191.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 191\" width=\"142\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions 3.7 Question 69\" width=\"420\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-69.png 420w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions-3.7-Question-69-300x114.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p>Question 70.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-192.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 192\" width=\"134\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-192.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 192\" width=\"134\" height=\"134\" \/><br \/>\nFrom the above graph,<br \/>\nThe given points are: (-3, 1), (1, -4)<br \/>\nWe know that,<br \/>\nThe slope of the give line when (x1, y1), (x2, y2) are given is:<br \/>\nm= \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\nSo,<br \/>\n(x1, y1) = (-3, 1) and (x2, y2) = (1, -4)<br \/>\nSo,<br \/>\nm = \\(\\frac{-4 &#8211; 1}{1 &#8211; [-3]}\\)<br \/>\nm = \\(\\frac{-5}{1 + 3}\\)<br \/>\nm = \\(\\frac{-5}{4}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: &#8211;\\(\\frac{5}{4}\\)<\/p>\n<h3><a id=\"Graphing_Linear_Functions_Performance_Task:_The_Cost_of_a_T-Shirt\"><\/a>Graphing Linear Functions Performance Task: The Cost of a T-Shirt<\/h3>\n<p><b>3.4\u20133.7 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-193.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 193\" width=\"644\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-193.png 644w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-193-300x67.png 300w\" sizes=\"(max-width: 644px) 100vw, 644px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 3.4<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-194.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 194\" width=\"605\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-194.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-194-300x15.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p><b>Section 3.5<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-195.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 195\" width=\"514\" height=\"27\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-195.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-195-300x16.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p><b>Section 3.6<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-196.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 196\" width=\"585\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-196.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-196-300x43.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p><b>Section 3.7<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-197.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 197\" width=\"639\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-197.png 639w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-197-300x15.png 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nExplain how you determined what units of measure to use for the horizontal and vertical axes in Exercise 37 on page 142.<br \/>\nAnswer:<br \/>\nIn Exercise 37 on page 142,<br \/>\nThe given function is:<br \/>\nd (t)= (1\/2)t + 6<br \/>\nWe know that,<br \/>\nThe horizontal axis represents the independent variable<br \/>\nThe vertical axis represents the dependent variable<br \/>\nSo,<br \/>\nThe horizontal axis represents the time<br \/>\nThe vertical axis represents the depth<\/p>\n<p>Question 2.<br \/>\nExplain your plan for solving Exercise 48 on page 153.<br \/>\nAnswer:<br \/>\nIn Exercise 48 on page 153,<br \/>\nThe profits of a school obtained by a school before playoffs and during the playoffs<br \/>\nSo,<br \/>\nFirst, plot the 2 equations in a coordinate plane and compare the functions in the coordinate plane<\/p>\n<p><b>Performance Task\u00a0<\/b><\/p>\n<p><b>The Cost of a T-Shirt<\/b><\/p>\n<p>You receive bids for making T-shirts for your class fundraiser from four companies. To present the pricing information, one company uses a table, one company uses a written description, one company uses an equation, and one company uses a graph. How will you compare the different representations and make the final choice? To explore the answers to this question and more, go to <img loading=\"lazy\" class=\"alignnone size-full wp-image-36476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-198.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 198\" width=\"85\" height=\"80\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-199.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 199\" width=\"245\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-199.png 245w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-199-207x300.png 207w\" sizes=\"(max-width: 245px) 100vw, 245px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Functions_Chapter_Review\"><\/a>Graphing Linear Functions Chapter Review<\/h3>\n<p><b>3.1 Functions<\/b> (pp. 103 &#8211; 110)<\/p>\n<p><b>Determine whether the relation is a function. Explain. <\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-200.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 200\" width=\"290\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-200.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 200\" width=\"290\" height=\"76\" \/><br \/>\nWe know that,<br \/>\nEvery input has exactly one output.<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nHence, from the table,<br \/>\nWe can conclude that the given table is a function<\/p>\n<p><b>Determine whether the relation is a function. Explain.\u00a0<\/b><\/p>\n<p>Question 1.<br \/>\n(0, 1), (5, 6), (7, 9)<br \/>\nAnswer:<br \/>\nThe given ordered pairs are:<br \/>\n(0, 1), (5, 6), (7, 9)<br \/>\nWe know that,<br \/>\nEvery input has exactly one output<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-201.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 201\" width=\"140\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-201.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 201\" width=\"140\" height=\"132\" \/><br \/>\nWe know that,<br \/>\nEvery input has exactly one output<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nNow,<br \/>\nFrom the graph,<br \/>\nThe input &#8216;2&#8217; has 2 outputs i.e., (2, 0), and (2, 2)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is not a function<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-202.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 202\" width=\"142\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nThe given relation is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-202.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 202\" width=\"142\" height=\"116\" \/><br \/>\nWe know that,<br \/>\nEvery input has exactly one output<br \/>\nx represents the input<br \/>\ny represents the output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given relation is a function<\/p>\n<p>Question 4.<br \/>\nThe function y = 10x + 100 represents the amount y (in dollars) of money in your bank account after you babysit for x hours.<br \/>\na. Identify the independent and dependent variables.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 10x + 100<br \/>\nWhere,<br \/>\ny represents the amount in dollars<br \/>\nx represents the number of hours<br \/>\nNow,<br \/>\nFrom the given function,<br \/>\nWE can say that<br \/>\nThe independent variable of the given function is: x<br \/>\nThe dependent variable of the given function is: y<\/p>\n<p>b. You babysit for 4 hours. Find the domain and range of the function.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 10x + 100<br \/>\nWhere,<br \/>\ny represents the amount in dollars<br \/>\nx represents the number of hours<br \/>\nIt is given that you babysit for 4 hours<br \/>\nSo,<br \/>\nThe given value of x is: 4<br \/>\nSo,<br \/>\nThe maximum value of y is:<br \/>\ny = 10 (4) + 100<br \/>\ny = 40 + 100<br \/>\ny = $140<br \/>\nWe know that,<br \/>\nThe amount and the time must not be the negative values<br \/>\nHence,<br \/>\nThe domain of the given function is: 0 \u2264 x \u2264 4<br \/>\nThe range of the give function is: 0 \u2264 y \u2264 140<\/p>\n<p><b>3.2 Linear Functions<\/b> (pp. 111\u2013120)<\/p>\n<p>Does the table or equation represent a linear or nonlinear function? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-203.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 203\" width=\"217\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nAs x increases by 4, y increases by different amounts. The rate of change is not constant.<br \/>\nSo,<br \/>\nThe function is nonlinear.<\/p>\n<p>b. y = 3x &#8211; 4<br \/>\nAnswer:<br \/>\nThe equation is in the form y = mx + b.<br \/>\nSo,<br \/>\nThe equation represents a linear function.<\/p>\n<p><b>Does the table or graph represent a linear or nonlinear function? Explain.\u00a0<\/b><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-204.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 204\" width=\"198\" height=\"77\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-204.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 204\" width=\"198\" height=\"77\" \/><br \/>\nFrom the given table,<br \/>\nThe difference between all the values of x is: 5<br \/>\nThe difference between all the values of y is: -3<br \/>\nSince there is a constant difference present between the values of x and the values of y,<br \/>\nThe given table is a linear function<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-205.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 205\" width=\"128\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-205.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 205\" width=\"128\" height=\"117\" \/><br \/>\nWe know that,<br \/>\nThe representation of a linear function in the graph is a &#8220;Straight line&#8221;<br \/>\nBut,<br \/>\nWe can say that the given graph is not a straight line from the graph<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given graph is a non-linear function<\/p>\n<p>Question 7.<br \/>\nThe function y = 60 &#8211; 8x represents the amount y (in dollars) of money you have after buying x movie tickets.<br \/>\n(a) Find the domain of the function. Is the domain discrete or continuous? Explain.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 60 &#8211; 8x<br \/>\nWhere,<br \/>\ny represents the amount in dollars<br \/>\nx represents the number of movie tickets<br \/>\nWe know that,<br \/>\nThe domain is the set of all the values of x so that the given function will be satisfied<br \/>\nSince x represents the number of movie tickets, the value of x can&#8217;t be negative and the number of tickets will be infinity<br \/>\nHence,<br \/>\nThe domain of the given function is: 0 \u2264 x \u2264 \u221e<br \/>\nHence, from the above domain,<br \/>\nWe can conclude that the domain is continuous<\/p>\n<p>(b) Graph the function using its domain. Evaluate the function when x = -3, 0 and 5.<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = 60 &#8211; 8x<br \/>\nNow,<br \/>\nThe value of the given function when x = -3 is:<br \/>\ny = 60 &#8211; 8 (-3)<br \/>\ny = 60 + 24<br \/>\ny = 84<br \/>\nThe value of the given function when x = 0 is:<br \/>\ny = 60 &#8211; 8 (0)<br \/>\ny = 60<br \/>\nThe value of the given function when x = 5 is:<br \/>\ny = 60 &#8211; 8(5)<br \/>\ny = 60 &#8211; 40<br \/>\ny = 20<br \/>\nNow,<br \/>\nThe representation of the given function along with its domain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-160.png\" alt=\"\" width=\"491\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-160.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-160-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-160-150x150.png 150w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = x + 8<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nf (x) = x + 8<br \/>\nWe know that,<br \/>\nThe standard representation of the function f (x) is: y<br \/>\nThe standard representation of the linear equation is:<br \/>\ny = mx + c<br \/>\nNow,<br \/>\ny = x + 8<br \/>\nBy comparing the given equation and the standard representation of the linear equation,<br \/>\nWe can conclude that the given equation is a linear equation<\/p>\n<p><strong>Find the value of x, so that the function has the given value.<\/strong><\/p>\n<p>Question 9.<br \/>\ng(x) = 4 &#8211; 3x<\/p>\n<p>Question 10.<br \/>\nk(x) = 7x; k(x) = 49<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nk (x) = 7x with k (x) = 49<br \/>\nSo,<br \/>\n49 = 7x<br \/>\nx = 49 \/ 7<br \/>\nx = 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 7<\/p>\n<p>Question 11.<br \/>\nr(x) = -5x &#8211; 1; r(x) = 19<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nr (x) = 5x &#8211; 1 with r (x) = 19<br \/>\nSo,<br \/>\n19 = 5x &#8211; 1<br \/>\n5x = 19 + 1<br \/>\n5x = 20<br \/>\nx = 20 \/ 5<br \/>\nx = 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the value of the given function is: 4<\/p>\n<p><b>Graph the linear function.<\/b><\/p>\n<p>Question 12.<br \/>\ng(x) = -2x &#8211; 3<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ng (x) = -2x &#8211; 3<br \/>\nHence,<br \/>\nThe representation of g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-161.png\" alt=\"\" width=\"491\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-161.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-161-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-161-150x150.png 150w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 13.<br \/>\nh(x) = \\(\\frac{2}{3}\\)x + 4<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nh (x) = \\(\\frac{2}{3}\\)x + 4<br \/>\nHence,<br \/>\nThe representation of h (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-162.png\" alt=\"\" width=\"502\" height=\"531\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-162.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-162-284x300.png 284w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 14.<br \/>\n8x &#8211; 4y = 16<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\n8x &#8211; 4y = 16<br \/>\n4y = 8x &#8211; 16<br \/>\ny = \\(\\frac{8x\u00a0 16}{4}\\)<br \/>\ny = \\(\\frac{8x}{4}\\) &#8211; \\(\\frac{16}{4}\\)<br \/>\ny =2x &#8211; 4<br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-163.png\" alt=\"\" width=\"490\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-163.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-163-292x300.png 292w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p><span style=\"font-size: 16px;\">Question 15.<br \/>\n<\/span>-12x &#8211; 3y = 36<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\n-12x &#8211; 3y = 36<br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-164.png\" alt=\"\" width=\"486\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-164.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-164-289x300.png 289w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 16.<br \/>\ny = -5<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\ny = -5<br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-165.png\" alt=\"\" width=\"498\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-165.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-165-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-165-150x150.png 150w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Question 17.<br \/>\nx = 6<br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nx = 6<br \/>\nHence,<br \/>\nThe representation of the given function in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-166.png\" alt=\"\" width=\"486\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-166.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-166-291x300.png 291w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><b>The points represented by the table lie on a line. Find the slope of the line.\u00a0<\/b><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-206.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 206\" width=\"102\" height=\"138\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-206.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 206\" width=\"102\" height=\"138\" \/><br \/>\nWe know that,<br \/>\nIf the input and output values are given in the form of the table,<br \/>\nWe can take any 2 pairs of the input and output values to find the slope<br \/>\nSo,<br \/>\nThe representation of ordered pairs to find the slope is:<br \/>\n(x1, y1) = (6, 9),<br \/>\n(x2, y2) = (11, 15)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{15 &#8211; 9}{11 &#8211; 6}\\)<br \/>\n= \\(\\frac{6}{5}\\)<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: \\(\\frac{6}{5}\\)<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-207.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 207\" width=\"109\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>The given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-207.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 207\" width=\"109\" height=\"138\" \/><br \/>\nWe know that,<br \/>\nIf the input and output values are given in the form of the table,<br \/>\nWe can take any 2 pairs of the input and output values to find the slope<br \/>\nSo,<br \/>\nThe representation of ordered pairs to find the slope is:<br \/>\n(x1, y1) = (3, -5),<br \/>\n(x2, y2) = (3, -2)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-2 &#8211; [-5]}{3 &#8211; 3}\\)<br \/>\n= \\(\\frac{5 &#8211; 2}{0}\\)<br \/>\n= Undefined or \u221e<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: Undefined or \u221e<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-208.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 208\" width=\"104\" height=\"153\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-208.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 208\" width=\"104\" height=\"153\" \/><br \/>\nWe know that,<br \/>\nIf the input and output values are given in the form of the table,<br \/>\nWe can take any 2 pairs of the input and output values to find the slope<br \/>\nSo,<br \/>\nThe representation of ordered pairs to find the slope is:<br \/>\n(x1, y1) = (-4, -1),<br \/>\n(x2, y2) = (-3, -1)<br \/>\nNow,<br \/>\nWe know that,<br \/>\nThe slope of the line = \\(\\frac{y2 &#8211; y1}{x2 &#8211; x1}\\)<br \/>\n= \\(\\frac{-1 &#8211; [-1]}{-3 &#8211; [-4]}\\)<br \/>\n= \\(\\frac{-1 + 1}{-3 + 4}\\)<br \/>\n= 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the slope of the given line is: 0<\/p>\n<p><b>Graph the linear equation. Identify the x-intercept.\u00a0<\/b><\/p>\n<p>Question 21.<br \/>\ny = 2x + 4<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\ny = 2x + 4<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\n2x + 4 = 0<br \/>\n2x = -4<br \/>\nx = -4 \/ 2<br \/>\nx = -2<br \/>\nHence,<br \/>\nThe representation of the given linear equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-167.png\" alt=\"\" width=\"479\" height=\"478\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-167.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-167-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-167-150x150.png 150w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 22.<br \/>\n-5x + y = -10<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\n-5x + y = -10<br \/>\nTo find the x-intercept, put y = 0<br \/>\n-5x + 0 = -10<br \/>\n-5x = -10<br \/>\n5x = 10<br \/>\nx = 10 \/ 5<br \/>\nx = 2<br \/>\nHence,<br \/>\nThe representation of the given linear equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-168.png\" alt=\"\" width=\"470\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-168.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-168-300x296.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 23.<br \/>\nx + 3y = 9<br \/>\nAnswer:<br \/>\nThe given linear equation is:<br \/>\nx + 3y = 9<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\nx + 0 = 9<br \/>\nx = 9<br \/>\nHence,<br \/>\nThe representation of the given linear equation in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-169.png\" alt=\"\" width=\"478\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-169.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-169-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-169-150x150.png 150w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 24.<br \/>\nA linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independent variable increases. Graph h when h(0) = 2. Identify the slope, y-intercept, and x-intercept of the graph. Let f(x) = 3x + 4. Graph f and h. Describe the transformation from the graph of f to the graph of h.<br \/>\nAnswer:<br \/>\nIt is given that a linear function h models a relationship in which the dependent variable decreases 2 units for every 3 units the independent variable increases.<br \/>\nWe know that,<br \/>\nx represents the independent variable<br \/>\ny represents the dependent variable<br \/>\nSo,<br \/>\nThe given x value is: 3<br \/>\nThe given y value is: -2<br \/>\nSo,<br \/>\nThe rate of change (or) slope (m) = \\(\\frac{y}{x}\\)<br \/>\n= \\(\\frac{-2}{3}\\)<br \/>\n= &#8211;\\(\\frac{2}{3}\\)<br \/>\nIt is also given that h (0) = 2<br \/>\nThat means the y-intercept of h (x) is 2 when x is 0<br \/>\nWe know that,<br \/>\nThe representation of the standad form of the linear equation is:<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nh (x) =-\\(\\frac{2}{3}\\)x + 2<br \/>\nThe other given function is:<br \/>\nf (x) = 3x + 4<br \/>\nHence,<br \/>\nThe representation of f (x0 and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-170.png\" alt=\"\" width=\"500\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-170.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-170-288x300.png 288w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) is 1.5 units away from f (x) on the x-axis<\/p>\n<p><strong>Let f(x) = 3x + 4.Graph f and h. Describe the transformation from the graph of f to the graph of h.<\/strong><\/p>\n<p>Question 25.<br \/>\nh(x) = f(x + 3)<br \/>\nANswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = f (x + 3)<br \/>\nSo,<br \/>\nh (x) = 3 (x + 3) + 4<br \/>\nh (x) = 3 (x) + 3 (3) + 4<br \/>\nh (x) = 3x + 9 + 4<br \/>\nh (x) = 3x + 13<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-171.png\" alt=\"\" width=\"479\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-171.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-171-286x300.png 286w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and h (x) are parallel lines<\/p>\n<p>Question 26.<br \/>\nh(x) = f(x) + 1<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = f (x) + 1<br \/>\nSo,<br \/>\nh (x) = 3x + 4 + 1<br \/>\nh (x) = 3x + 5<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-172.png\" alt=\"\" width=\"501\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-172.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-172-300x296.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and h (x) are the paralel lines<\/p>\n<p>Question 27.<br \/>\nh(x) = f(-x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = f (-x)<br \/>\nSo,<br \/>\nh (x) = 3 (-x) + 4<br \/>\nh (x) = -3x + 4<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-173.png\" alt=\"\" width=\"487\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-173.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-173-293x300.png 293w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) and f (x) are inversions of each other<\/p>\n<p>Question 28.<br \/>\nh(x) = -f(x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = -f (x)<br \/>\nSo,<br \/>\nh (x) = &#8211; (3x + 4)<br \/>\nh (x) = -3x &#8211; 4<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-174.png\" alt=\"\" width=\"500\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-174.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-174-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-174-150x150.png 150w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) and f (x) are reflections to each other<\/p>\n<p>Question 29.<br \/>\nh(x) = 3f(x)<br \/>\nAnswer:<br \/>\nThe given function srae:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = 3 f (x)<br \/>\nSo,<br \/>\nh (x) = 3 (3x + 4)<br \/>\nHence,<br \/>\nThe representation of f (x) and\u00a0 h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-175.png\" alt=\"\" width=\"485\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-175.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-175-293x300.png 293w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) is a vertical stretch of f (x)<\/p>\n<p>Question 30.<br \/>\nh(x) = f(6x)<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = 3x + 4<br \/>\nh (x) = f (6x)<br \/>\nSo,<br \/>\nh (x) = 3 (6x) + 4<br \/>\nh (x) = 18x + 4<br \/>\nHence,<br \/>\nThe representation of f (x) and h (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-176.png\" alt=\"\" width=\"479\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-176.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-176-293x300.png 293w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that h (x) translates 2 units away from f (x) on the x-axis<\/p>\n<p>Question 31.<br \/>\nGraph f(x) = x and g(x) = 5x + 1. Describe the transformations from the graph of f to the graph of g.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = x<br \/>\ng (x) = 5x + 1<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-177.png\" alt=\"\" width=\"487\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-177.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-177-293x300.png 293w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates away 8 units away from f (x)\u00a0 on the x-axis<\/p>\n<p><b>Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range.<\/b><\/p>\n<p>Question 32.<br \/>\nm(x) = | x | + 6<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nm (x) = | x | + 6<br \/>\nHence,<br \/>\nThe representation of f (x) and m (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-178.png\" alt=\"\" width=\"490\" height=\"509\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-178.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-178-289x300.png 289w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\nHene, from the above,<br \/>\nWe can conclude that m (x) translates 6 units up from the positive x-axis<br \/>\nHence,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of m (x) is: -4 \u2264 x \u2264 4<br \/>\nThe range of m (x) is: 0 \u2264y \u2264 10<br \/>\nThe range of f (x) is: 0 \u2264 y \u226410<br \/>\nThe range of m (x) is: 6 \u2264y \u226410<\/p>\n<p>Question 33.<br \/>\np(x) = | x &#8211; 4 |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\np (x) = | x &#8211; 4 |<br \/>\nHence,<br \/>\nThe representation of f (x) and p (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-179.png\" alt=\"\" width=\"562\" height=\"496\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-179.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-179-300x265.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\nHene, from the above,<br \/>\nWe can conclude that p (x) translates 1 unit up from the positive x-axis<br \/>\nHence,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of p (x) is: -6 \u2264 x \u2264 10<br \/>\nThe range of f (x) is: 0 \u2264 y \u226410<br \/>\nThe range of p (x) is: 6 \u2264y \u226410<\/p>\n<p>Question 34.<br \/>\nq(x) = 4 | x |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nq (x) = 4 | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and q (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-180.png\" alt=\"\" width=\"493\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-180.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-180-296x300.png 296w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nHene, from the above,<br \/>\nWe can conclude that q (x) translates 7 units up from the positive x-axis<br \/>\nHence,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of q (x) is: -2.5 \u2264 x \u2264 2.5<br \/>\nThe range of q (x) is: 0 \u2264y \u2264 10<br \/>\nThe range of f (x) is: 0 \u2264 y \u226410<\/p>\n<p>Question 35.<br \/>\nr(x) = &#8211;\\(-\\frac{1}{4}\\)| x |<br \/>\nAnswer:<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\nr (x) = &#8211;\\(-\\frac{1}{4}\\) | x |<br \/>\nSo,<br \/>\nr (x) = \\(\\frac{1}{4}\\) | x |<br \/>\nHence,<br \/>\nThe representation of f (x) and r (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-181.png\" alt=\"\" width=\"503\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-181.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-181-285x300.png 285w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\nHene, from the above,<br \/>\nWe can conclude that r (x) translates\u00a0 units up from the positive x-axis<br \/>\nHence,<br \/>\nThe domain of f (x) is: -10 \u2264 x \u2264 10<br \/>\nThe domain of r (x) is: -10 \u2264 x \u2264 10<br \/>\nThe range of r (x) is: 0 \u2264y \u2264 2<br \/>\nThe range of f (x) is: 0 \u2264 y \u226410<\/p>\n<p>Question 36.<br \/>\nGraph f(x) = | x &#8211; 2 | + 4 and g(x) = | 3x &#8211; 2 | + 4. Compare the graph of g to the graph of f.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x &#8211; 2 | + 4<br \/>\ng (x) = | 3x &#8211; 2 | + 4<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the same coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-182.png\" alt=\"\" width=\"481\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-182.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-182-290x300.png 290w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates 5 units away from f (x) on the x-axis<\/p>\n<p>Question 37.<br \/>\nLet g(x) = \\(\\frac{1}{3}\\) | x &#8211; 1 | &#8211; 2.<br \/>\n(a) Describe the transformations from the graph of f(x) = | x | to the graph of g.<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\ng (x) = \\(\\frac{1}{3}\\) | x &#8211; 1 | &#8211; 2<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-183.png\" alt=\"\" width=\"489\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-183.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-183-283x300.png 283w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) translates 2 units away from f (x) on the y-axis<br \/>\n(b) Graph g.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\ng (x) = \\(\\frac{1}{3}\\) | x &#8211; 1 | &#8211; 2<br \/>\nHence,<br \/>\nThe representation of g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-184.png\" alt=\"\" width=\"489\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-184.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-184-281x300.png 281w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<h3><a id=\"Graphing_Linear_Functions_Chapter_Test\"><\/a>Graphing Linear Functions Chapter Test<\/h3>\n<p><b>Determine whether the relation is a function. If the relation is a function, determine whether the function is linear or nonlinear. Explain.\u00a0<\/b><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-209.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 209\" width=\"195\" height=\"72\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-209.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 209\" width=\"195\" height=\"72\" \/><br \/>\nWe know that,<br \/>\nEvery input has exactly one output<br \/>\nSo,<br \/>\nThe given table is a function<br \/>\nNow,<br \/>\nThe constant between all the values of x is: 1<br \/>\nThere is no constant difference between all the values of y<br \/>\nSince there is no constant rate of change,<br \/>\nWe can conclude that the obtained function is a non-linear function<\/p>\n<p>Question 2.<br \/>\ny = -2x + 3<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = -2x + 3<br \/>\nWe know that,<br \/>\nThe standard form of the linear equation is:<br \/>\ny = mx + c<br \/>\nFor a relation o be a function, every input has exactly only one output<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given equation is a function and it is a linear function<\/p>\n<p>Question 3.<br \/>\nx = -2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\nx = -2<br \/>\nWe know that,<br \/>\nA relation is said to be a function if every input has exactly one output<br \/>\nSo,<br \/>\nFor x = -2<br \/>\nThe input is: 2<br \/>\nThe output is: 0<br \/>\nSo,<br \/>\nThe given equation is a function<br \/>\nFor a given function to be a linear function, it will be in the form<br \/>\ny = mx + c<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given function is a non-linear function<\/p>\n<p><b>Graph the equation and identify the intercept(s). If the equation is linear, find the slope of the line.\u00a0<\/b><\/p>\n<p>Question 4.<br \/>\n2x &#8211; 3y = 6<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\n2x &#8211; 3y = 6<br \/>\n3y = 2x &#8211; 6<br \/>\ny = \\(\\frac{2x &#8211; 6}{3}\\)<br \/>\ny = \\(\\frac{2x}{3}\\) &#8211; \\(\\frac{6}{3}\\)<br \/>\ny = \\(\\frac{2}{3}\\)x &#8211; 2<br \/>\nHence,<br \/>\nThe above equation is in the form of<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nThe given equation is a linear equation<br \/>\nSo,<br \/>\nm = \\(\\frac{2}{3}\\)<br \/>\nThe y-intercept is: -2<br \/>\nTo find the x-intercept, put y = 0<br \/>\n\\(\\frac{2}{3}\\)x &#8211; 2 = 0<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nSlope (m) = \\(\\frac{2}{3}\\)<br \/>\nThe x-intercept is: 3<br \/>\nThe y-intercept is: -2<\/p>\n<p>Question 5.<br \/>\ny = 4.5<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = 4.5<br \/>\nThe given equation is not in the form of<br \/>\ny = mx + c<br \/>\nHence,<br \/>\nThe given equation is non-linear<\/p>\n<p>Question 6.<br \/>\ny = | x &#8211; 1 | &#8211; 2<br \/>\nAnswer:<br \/>\nThe given equation is:<br \/>\ny = | x &#8211; 1 | &#8211; 2<br \/>\nWe know that,<br \/>\n| x | = x for x &gt; 0<br \/>\n| x | = -x for x &lt; 0<br \/>\nSo,<br \/>\ny = x &#8211; 1 &#8211; 2 or y = -(x &#8211; 1) &#8211; 2<br \/>\ny = x &#8211; 3 or y = -x + 1 &#8211; 2<br \/>\ny = x &#8211; 3 or y = -x &#8211; 1<br \/>\nThe above 2 equations are in the form of<br \/>\ny = mx + c<br \/>\nHence,<br \/>\nThe slope is: 1 or -1<br \/>\nThe y-intercept is: -3 or -1<br \/>\nTo find the x-intercept, put y =0<br \/>\nSo,<br \/>\n0 = x &#8211; 3 or 0 = -x &#8211; 1<br \/>\nx = 3 or x = -1<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope is: 1 or -1<br \/>\nThe x-intercept is: 3 or -1<br \/>\nThe y-intercept is: -3 or -1<\/p>\n<p><b>Find the domain and range of the function represented by the graph. Determine whether the domain is discrete or continuous. Explain.\u00a0<\/b><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-210.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 210\" width=\"164\" height=\"159\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-210.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 210\" width=\"164\" height=\"159\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the graph is not a straight line<br \/>\nSo,<br \/>\nWe can say that the given graph is a non-linear function<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain is continuous by observing the graph<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-211.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 211\" width=\"169\" height=\"164\" \/><br \/>\nAnswer:<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-211.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 211\" width=\"169\" height=\"164\" \/><br \/>\nFrom the graph,<br \/>\nWe can observe that the points form a straight line<br \/>\nSo,<br \/>\nWe can say that the given graph is a linear function<br \/>\nHence, from the above,<br \/>\nWe can conclude that the domain is continuous since all the points are connected<\/p>\n<p><b>Graph f and g. Describe the transformations from the graph of f to the graph of g.\u00a0<\/b><\/p>\n<p>Question 9.<br \/>\nf(x) = x; g(x) = -x + 3<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = x<br \/>\ng (x) = -x + 3<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-185.png\" alt=\"\" width=\"492\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-185.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-185-293x300.png 293w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that f (x) and g (x) are perpendicular lines with a slope of -1<\/p>\n<p>Question 10.<br \/>\nf(x) = | x | ; g(x) = | 2x + 4 |<br \/>\nAnswer:<br \/>\nThe given functions are:<br \/>\nf (x) = | x |<br \/>\ng (x) = | 2x + 4 |<br \/>\nHence,<br \/>\nThe representation of f (x) and g (x) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-186.png\" alt=\"\" width=\"499\" height=\"501\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-186.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-186-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-186-150x150.png 150w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that g (x) is 2 units away from f (x) on the x-axis<\/p>\n<p>Question 11.<br \/>\nFunction A represents the amount of money in a jar based on the number of quarters in the jar. Function B represents your distance from home over time. Compare the domains.<br \/>\nAnswer:<br \/>\nIt is given that<br \/>\nFunction A represents the amount of money in a jar based on the number of quarters in the jar<br \/>\nFunction B represents your distance from home over time<br \/>\nWe know that,<br \/>\nThe distance should be greater than or equal to 0<br \/>\nThe amount is greater than or equal to a quarter of the amount of the money<br \/>\nHence,<br \/>\nThe domain of function A is: \\(\\frac{1}{4}\\) \u2264 x \u2264 \u221e<br \/>\nThe domain of function B is: 0 \u2264 x \u2264 \u221e<\/p>\n<p>Question 12.<br \/>\nA mountain climber is scaling a 500-foot cliff. The graph shows the elevation of the climber over time.<br \/>\na. Find and interpret the slope and the y-intercept of the graph.<br \/>\nb. Explain two ways to find f(3). Then find f(3) and interpret its meaning.<br \/>\nc. How long does it take the climber to reach the top of the cliff? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-212.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 212\" width=\"234\" height=\"173\" \/><br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that a mountain-climber is scaling a 500-foot cliff<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-212.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 212\" width=\"234\" height=\"173\" \/><br \/>\nFrom the graph,<br \/>\nThe equation that shows the elevation of the climber over tie is:<br \/>\nf (x) = 125x + 50<br \/>\nWe know that,<br \/>\nThe standard representation of the output for the function output is: y<br \/>\nSo,<br \/>\ny = 125x + 50<br \/>\nCompare the above equation with<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nm = 125 and the y-intercept is: 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that<br \/>\nThe slope of the given equation is: 125<br \/>\nThe y-intercept of the given equation is: 50<\/p>\n<p>b.<br \/>\nFrom part (a),<br \/>\nThe given equation is:<br \/>\nf (x) = 125x + 50<br \/>\nSo,<br \/>\nf (3) = 125 (3) + 50<br \/>\nf (3) = 375 + 50<br \/>\nf (3) = 425<br \/>\nHence, from the above,<br \/>\nWe can conclude that for 3 hours, the climber climbs 425 feet<\/p>\n<p>c.<br \/>\nThe given graph is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-212.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 212\" width=\"234\" height=\"173\" \/><br \/>\nFrom the given graph,<br \/>\nThe top of the hill is the maximum height i.e., the highest value on the y-axis<br \/>\nHence, from the above,<br \/>\nWe can conclude that it takes 4 hours to reach the top of the cliff<\/p>\n<p>Question 13.<br \/>\nWithout graphing, compare the slopes and the intercepts of the graphs of the functions f(x) = x + 1 and g(x) = f(2x).<br \/>\nAnswer:<br \/>\nThe given functons are:<br \/>\nf (x) = x + 1<br \/>\ng (x) = f (2x)<br \/>\nSo,<br \/>\ng (x) = 2x + 1<br \/>\nNow,<br \/>\nCompare f (x) and g (x) with the standard linear equation<br \/>\ny = mx + c<br \/>\nSo,<br \/>\nFor f (x),<br \/>\nm = 1 and c = 1<br \/>\nWhere,<br \/>\nc is the y-intercept<br \/>\nFor g (x),<br \/>\nm = 2 and c = 1<br \/>\nWhere,<br \/>\nc is the y-intercept<\/p>\n<p>Question 14.<br \/>\nA rock band releases a new single. Weekly sales s (in thousands of dollars) increase and then decrease as described by the function s(t) = -2 | t &#8211; 20 | + 40, where t is the time (in weeks).<br \/>\na. Identify the independent and dependent variables.<br \/>\nb. Graph s. Describe the transformations from the graph of f(x) = | x | to the graph of s.<br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that a rock band releases a new single and weekly sales s (in thousands of dollars) increase and then decrease as described by the function<br \/>\ns(t) = -2 | t &#8211; 20 | + 40<br \/>\nwhere,<br \/>\nt is the time (in weeks)<br \/>\nNow,<br \/>\nThe independent variable of the given function\u00a0 is: t<br \/>\nThe dependent variable of the given function is: s (t)<\/p>\n<p>b.<br \/>\nThe given absolute value functions are:<br \/>\nf (x) = | x |<br \/>\ns (t) = -2 | t &#8211; 20 | + 40<br \/>\nHence,<br \/>\nThe representation of f (x) and s (t) in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-187.png\" alt=\"\" width=\"488\" height=\"509\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-187.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-187-288x300.png 288w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that s (t) translates 5 units away from f (x) on the y-axis<\/p>\n<h3><a id=\"Graphing_Linear_Functions_Cumulative_Assessment\"><\/a>Graphing Linear Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nYou claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function. Using the given numbers, what values can you use for x (the input) and y (the output) to support your claim? What values can your friend use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-213.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 213\" width=\"543\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-213.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-213-300x119.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><br \/>\nAnswer:<br \/>\nIt is given that you claim you can create a table of values that represents a linear function. Your friend claims he can create a table of values that represents a nonlinear function.<br \/>\nHence,<br \/>\nThe values you and your friend use are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31.jpg\" alt=\"\" width=\"555\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31.jpg 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-31-300x52.jpg 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 2.<br \/>\nA car rental company charges an initial fee of $42 and a daily fee of $12.<br \/>\na. Use the numbers and symbols to write a function that represents this situation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-214.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 214\" width=\"344\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-214.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-214-300x95.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nb. The bill is $138. How many days did you rent the car?<br \/>\nAnswer:<br \/>\na.<br \/>\nIt is given that a car rental company charges an initial fee of $42 and a daily fee of $12<br \/>\nSo,<br \/>\nThe function that represents the situation is:<br \/>\nf (x) = (42 + 12) \u00d7 x<br \/>\nf (x) = 52x<br \/>\nWhere,<br \/>\nx is the number of days that you rent the car<\/p>\n<p>b.<br \/>\nIt is given that the bill is: $138<br \/>\nSo,<br \/>\n138 = 52x<br \/>\nx = 138 \u00f7 52<br \/>\nx = 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that you can rent the car for 3 days<\/p>\n<p>Question 3.<br \/>\nFill in values for a and b so that each statement is true for the inequality ax \u2212 b&gt; 0.<br \/>\na. When a = _____ and b = _____, x &gt; \\(\\frac{b}{a}\\).<br \/>\nb. When a = _____ and b = _____, x &lt; \\(\\frac{b}{a}\\).<br \/>\nAnswer:<br \/>\na.<br \/>\nThe given inequality is:<br \/>\nax &#8211; b &gt; 0<br \/>\nax &gt; b<br \/>\nx &gt; b \/ a<br \/>\nSo,<br \/>\nThe value of a is less than b and the value of b is greater than a<br \/>\nb.<br \/>\nThe value of a is greater than b and the value of b is less than a<\/p>\n<p>Question 4.<br \/>\nFill in the inequality with &lt;, \u2264, &gt;, or \u2265 so that the solution of the inequality is represented by the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 215\" width=\"388\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215-300x72.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nAnswer:<br \/>\nThe given number line is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 215\" width=\"388\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-215-300x72.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nFrom the given number line,<br \/>\nThe given inequality is:<br \/>\n-3 (x + 7) _____ -24<br \/>\n-3 (x) &#8211; 3 (7) _____ -24<br \/>\n-3x &#8211; 21 _____ -24<br \/>\n-3x ____ -24 + 21<br \/>\n-3x ____-3<br \/>\n3x ____ 3<br \/>\nx ____ 3 \/ 3<br \/>\nx ____ 1<br \/>\nFrom the number line<br \/>\nThe marked line represented from 1 including 1 and continued till the right end of the number line<br \/>\nHence,<br \/>\nx \u2265 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the symbol used for the given inequality is: \u2265<\/p>\n<p>Question 5.<br \/>\nUse the numbers to fill in the coefficients of ax + by = 40 so that when you graph the function, the x-intercept is -10 and the y-intercept is 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-216.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 216\" width=\"514\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-216.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-216-300x34.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nax + by = 40<br \/>\nIt is given that the x-intercept and the y-intercept is: -10 and 8<br \/>\nNow,<br \/>\nTo find the x-intercept, put y = 0<br \/>\nSo,<br \/>\nax = 40<br \/>\na (-10) = 40<br \/>\na = -40 \/ 10<br \/>\na = -4<br \/>\nTo find the y-intercept, put x = 0<br \/>\nSo,<br \/>\nby = 40<br \/>\nb (8) = 40<br \/>\nb = 40 \/ 8<br \/>\nb = 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the values of a and b are: -4 and 5<\/p>\n<p>Question 6.<br \/>\nSolve each equation. Then classify each equation based on the solution. Explain your reasoning.<br \/>\na. 2x &#8211; 9 = 5x &#8211; 33<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n2x &#8211; 9 = 5x &#8211; 33<br \/>\n2x &#8211; 5x = -33 + 9<br \/>\n-3x = -24<br \/>\nx = 24 \/ 3<br \/>\nx = 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has 1 solution<\/p>\n<p>b. 5x &#8211; 6 = 10x + 10<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n5x &#8211; 6 = 10x + 10<br \/>\n5x &#8211; 10x = 10 + 6<br \/>\n-5x = 16<br \/>\nx = -16 \/ 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has only 1 solution<\/p>\n<p>c. 2(8x &#8211; 3) = 4(4x + 7)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n2 (8x &#8211; 3 ) = 4 (4x + 7)<br \/>\n2 (8x) &#8211; 2 (3) = 4 (4x) + 4(7)<br \/>\n16x &#8211; 6 = 16x + 28<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has no solution<\/p>\n<p>d. -7x + 5 = 2(x &#8211; 10.1)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n-7x + 5 = 2 (x &#8211; 10.1)<br \/>\n-7x + 5 = 2x &#8211; 20.2<br \/>\n-7x &#8211; 2x = -20.2 &#8211; 5<br \/>\n-9x = -25.2<br \/>\nx = 25.9 \/ 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has only 1 solution<\/p>\n<p>e. 6(2x + 4) = 4(4x + 10)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n6 (2x + 4) = 4 (4x + 10)<br \/>\n12x + 24 = 16x + 40<br \/>\n12x &#8211; 16x = 40 &#8211; 24<br \/>\n-4x = 16<br \/>\nx = -16 \/ 4<br \/>\nx = -4<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has only 1 solution<\/p>\n<p>f. 8(3x + 4) = 2(12x + 16)<br \/>\nAnswer:<br \/>\nThe given expression is:<br \/>\n8 (3x + 4) = 2 (12x + 16)<br \/>\n24x + 32 = 24x + 32<br \/>\nHence, from the above,<br \/>\nWe can conclude that the given expression has no solution<\/p>\n<p>Question 7.<br \/>\nThe table shows the cost of bologna at a deli. Plot the points represented by the table in a coordinate plane. Decide whether you should connect the points with a line. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 217\" width=\"355\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217-300x66.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nAnswer:<br \/>\nThe given table is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 217\" width=\"355\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-217-300x66.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nHence,<br \/>\nThe representation of the points in the coordinate plane is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-64933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-188.png\" alt=\"\" width=\"493\" height=\"505\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-188.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-188-293x300.png 293w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\nHence, from the above,<br \/>\nWe can say that we can connect the points in the graph<\/p>\n<p>Question 8.<br \/>\nThe graph of g is a horizontal translation right, then a vertical stretch, then a vertical translation down of the graph of f(x) = x. Use the numbers and symbols to create g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-218.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 218\" width=\"452\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-218.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-218-300x74.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><br \/>\nAnswer:<br \/>\nThe given function is:<br \/>\nf (x) = x<br \/>\nWe know that,<br \/>\nf (x) can be re-written as f<br \/>\ng (x) can b ere-written as g<br \/>\nNow,<br \/>\nLet the operations performed on f (x) can be expressed in terms of g (x)<br \/>\nSo,<br \/>\nHorizontal translation right:<br \/>\ng (x) = f (x) &#8211; 3 or g (x) = f (x) &#8211; 1 or g (x)\u00a0 f (x) &#8211; (1\/2)<br \/>\nVertical stretch:<br \/>\ng (x) = 3 f (x)<br \/>\nVertical translation down:<br \/>\ng (x) = f (x &#8211; 1)<\/p>\n<p>Question 9.<br \/>\nWhat is the sum of the integer solutions of the compound inequality 2 | x &#8211; 5 | &lt; 16?<br \/>\nA. 72<br \/>\nB. 75<br \/>\nC. 85<br \/>\nD. 88<br \/>\nAnswer:<br \/>\nThe given compound inequality is:<br \/>\n2 | x &#8211; 5 | &lt; 16<br \/>\nSo,<br \/>\n2 (x &#8211; 5) &lt; 16 an d 2 (x &#8211; 5 ) &gt; -16<br \/>\n2x &#8211; 10 &lt; 16 and 2x &#8211; 10 &gt; -16<br \/>\n2x &lt; 26 and 2x &gt;-6<br \/>\nx &lt; 13 and x &gt; -3<br \/>\nHence,<br \/>\nThe solution of the given compoud inequality is: -3 &lt; x &lt; 13<br \/>\nNow,<br \/>\nThe sum of all the integers = -2 &#8211; 1 + 0 + 1 + 2 + 3 + 4 + 5+ 6 + 7 + 8 +9 + 10 + 11 + 12<br \/>\n= 75<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of all the integers is: 75<\/p>\n<p>Question 10.<br \/>\nYour bank offers a text alert service that notifies you when your checking account balance drops below a specific amount. You set it up so you are notified when your balance drops below $700. The balance is currently $3000. You only use your account for paying your rent (no other deposits or deductions occur). Your rent each month is $625.<br \/>\na. Write an inequality that represents the number of months m you can pay your rent without receiving a text alert.<br \/>\nAnswer:<br \/>\nIt is given that your bank offers a text alert service that notifies you when your checking account balance drops below a specific amount. You set it up so you are notified when your balance drops below $700. The balance is currently $3000. You only use your account for paying your rent (no other deposits or deductions occur). Your rent each month is $625<br \/>\nLet m be the number of months<br \/>\nHence,<br \/>\nThe inequality that represents the number of months you can pay rent without receiving a text is:<br \/>\n3000 &#8211; 625x &gt; 700<\/p>\n<p>b. What is the maximum number of months you can pay your rent without receiving a text alert?<br \/>\nAnswer:<br \/>\nFrom part (a),<br \/>\nThe inequality that represents the number of months m without receiving a text alert is:<br \/>\n3000 &#8211; 625x &gt; 700<br \/>\n3000 &#8211; 700 &gt; 625x<br \/>\n2300 &gt; 625x<br \/>\n2300 \/ 625 &gt; x<br \/>\n3.68 &gt; x<br \/>\nx &lt; 4 months [ Since the number of months will not be in decimals]<br \/>\nHence, from the above,<br \/>\nWe can conclude that the maximum number of months you can pay your rent without receiving a text alert is: 4 months<\/p>\n<p>c. Suppose you start paying rent in June. Select all the months you can pay your rent without making a deposit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-219.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 3 Graphing Linear Functions 219\" width=\"515\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-219.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-3-Graphing-Linear-Functions-219-300x38.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><br \/>\nAnswer:<br \/>\nFrom part (b),<br \/>\nThe maximum number of months is:<br \/>\nx &lt; 4 months<br \/>\nIt is given that you start paying rent in June<br \/>\nSo,<br \/>\nAll the months you can pay your rent without making a deposit is:<br \/>\nJune, July, August<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kids who are passionate about solving math calculations and enhance their math skills can refer to this guide. Here we have shared the Topic wise Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions free pdf. In this BIM Textbook Solution Key of Algebra 1 Ch 3 Graphing Linear functions, you can find &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-3\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 3 Graphing Linear Functions\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":89205,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-3-Graphing-Linear-Functions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35937"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35937"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35937\/revisions"}],"predecessor-version":[{"id":90354,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35937\/revisions\/90354"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89205"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35937"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35937"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}