{"id":31757,"date":"2024-01-03T10:31:53","date_gmt":"2024-01-03T05:01:53","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=31757"},"modified":"2024-01-03T17:47:32","modified_gmt":"2024-01-03T12:17:32","slug":"big-ideas-math-answers-grade-8-chapter-7","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-7\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 7 Functions"},"content":{"rendered":"<p>Big Ideas Math Grade 8 Chapter 7 Functions is given by subject experts adhering to the latest syllabus guidelines. Become Proficient in the Concepts of Big Ideas Math Grade 8 Functions by consistently practicing from our BIM Book 8th Grade Ch 7 Functions Answer Key. To make it easy for you to understand the concepts we have provided step-by-step solutions in the <strong>Big Ideas Math Answers Grade 8<\/strong> Chapter 7 Functions. You can download the quick resources without even paying a single penny.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 7 Functions<\/h2>\n<p>Big Ideas Math Grade 8 Ch 7 Functions Solutions provided here cover the questions from Lessons 7.1 to 7.5, Practice Tests, Review Tests, Cumulative Practice, Assessment Tests, etc. You can have deeper insights into all the Topics of Functions such as the representation of functions, linear functions, analyzing and sketching graphs, etc. Use the below available quick links for Big Ideas Math 8th Grade Chapter 7 Functions Answer Key and clear all your ambiguities regarding the concerned topics.<\/p>\n<p><strong>STEAM Video\/Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#STEAM _Video\/_Performance _Task\">STEAM Video\/Performance Task<\/a><\/li>\n<\/ul>\n<p><strong>Getting Ready for Chapter 7<\/strong><\/p>\n<ul>\n<li><a href=\"#Getting _Ready _for _Chapter _7\">Getting Ready for Chapter 7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 1 Relations and Functions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson _7.1 _Relations _and _Functions\">Lesson 7.1 Relations and Functions<\/a><\/li>\n<li><a href=\"#Relations _and _Functions _Homework _&amp; _Practice _7.1\">Relations and Functions Homework &amp; Practice 7.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2 Representations of Functions\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson _7.2 _Representations _of _Functions\">Lesson 7.2 Representations of Functions<\/a><\/li>\n<li><a href=\"#Representations _of _Functions _Homework _&amp; _Practice _7.2\">Representations of Functions Homework &amp; Practice 7.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3 Linear Functions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson _7.3 _Linear _Functions\">Lesson 7.3 Linear Functions<\/a><\/li>\n<li><a href=\"#Linear _Functions _Homework _&amp; _Practice _7.3\">Linear Functions Homework &amp; Practice 7.3\u00a0<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4 Comparing Linear and Non Linear Functions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson _7.4 _Comparing _Linear _and _Non _Linear _Functions\">Lesson 7.4 Comparing Linear and Non Linear Functions<\/a><\/li>\n<li><a href=\"#Comparing _Linear _and _Non _Linear _Functions _Homework _&amp; _Practice _7.4\">Comparing Linear and Non Linear Functions Homework &amp; Practice 7.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5 Analyzing and Sketching Graphs<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson _7.5 _Analyzing _and _Sketching _Graphs\">Lesson 7.5 Analyzing and Sketching Graphs<\/a><\/li>\n<li><a href=\"#Analyzing _and _Sketching _Graphs _Homework _&amp; _Practice _7.5\">Analyzing and Sketching Graphs Homework &amp; Practice 7.5<\/a><\/li>\n<\/ul>\n<p><strong>Functions Connecting Concepts<\/strong><\/p>\n<ul>\n<li><a href=\"#Functions _Connecting _Concepts\">Functions Connecting Concepts<\/a><\/li>\n<li><a href=\"#Functions _Chapter _Review\">Functions Chapter Review<\/a><\/li>\n<li><a href=\"#Functions _Practice _Test\">Functions Practice Test<\/a><\/li>\n<li><a href=\"#Functions _Cumulative _Practice\">Functions Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"STEAM _Video\/_Performance _Task\"><\/a>Functions STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Apparent Temperature<br \/>\nSometimes it feels hotter or colder outside than the actual apparent temperature. How hot or cold it feels is called the temperature. What weather factors might contribute to the apparent temperature?<br \/>\nWatch the STEAM Video \u201cApparent Temperature.\u201d Then answer the following questions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 1\" width=\"175\" height=\"190\" \/><br \/>\n1. Robert says that the Wet-Bulb Globe Temperature (WBGT)index is used as a measure of apparent temperature.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 2\" width=\"300\" height=\"220\" \/><br \/>\nIn the formula, T<sub>W<\/sub> is the natural wet-bulb temperature, T<sub>G<\/sub> is the black-globe temperature, T<sub>D<\/sub> and is the dry-bulb temperature. Find WBGT when T<sub>W<\/sub> = 75\u00baF, T<sub>G<\/sub> = 100\u00baF, and T<sub>D<\/sub> = 84\u00baF.<br \/>\n2. Different categories of Wet-Bulb Globe Temperatures are shown in the chart. Each category can be represented by a different-colored \ufb02ag. Which flag color is displayed when WGBT = 87.5\u00baF?<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Heat Index<br \/>\nAfter completing this chapter, you will be able to use the STEAM concepts you learned to answer the questions in the Video Performance Task. You will be given information about heat index.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 3\" width=\"592\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-3.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-3-300x166.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><br \/>\nYou will be asked to create a graph of the temperatures and heat indices. Why is it useful to know the heat index?<\/p>\n<h3><a id=\"Getting _Ready _for _Chapter _7\"><\/a>Functions Getting Ready for Chapter 7<\/h3>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Work with a partner. Copy and complete the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 4\" width=\"481\" height=\"558\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-4.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-4-259x300.png 259w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>1.\u00a0 Answer: ( 1 , 2 ) , ( 2 , 4 ) , ( 3 , 6 ) , ( 4 , 8 ) .<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-1.png\" alt=\"\" width=\"151\" height=\"136\" \/><br \/>\nGiven , Width w = 2 , Length l = x\u00a0 where x = 1 , 2 , 3 , 4 .<br \/>\nTo find Area A of a rectangle we have , A = w \u00d7 l<br \/>\nfor x = 1 , A = 2 \u00d7 1 = 2 ,<br \/>\nfor x = 2 , A = 2 \u00d7 2 = 4 ,<br \/>\nfor x = 3 , A = 2 \u00d7 3 = 6 ,<br \/>\nfor x = 4 , A = 2 \u00d7 4 = 8 ,<br \/>\nSo, for every value of Input x = 1 , 2 , 3 , 4 we have Output A = 2 , 4 , 6 , 8 , respectively .<br \/>\nThat is ( 1 , 2 ) , ( 2 , 4 ) , ( 3 , 6 ) , ( 4 , 8 ) .<\/p>\n<p>2. Answer: ( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 ) , ( 4 , 12 ).<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-2.png\" alt=\"\" width=\"152\" height=\"133\" \/><br \/>\nGiven , Width w = 2 , Length l = x\u00a0 where x = 1 , 2 , 3 , 4 .<br \/>\nTo find Perimeter of a rectangle we have , P = 2( l + w )<br \/>\nfor x = 1 ,P = 2( 1 + 2 ) = 2 \u00d7 3 = 6 ,<br \/>\nfor x = 2 , P = 2( 2 + 2 ) = 2 \u00d7 4 = 8\u00a0 ,<br \/>\nfor x = 3 , P = 2( 3 + 2 ) = 2 \u00d7 5 = 10\u00a0 ,<br \/>\nfor x = 4 , P = 2( 4 + 2 ) = 2 \u00d7 6 = 12\u00a0 ,<br \/>\nSo, for every value of Input x = 1 , 2 , 3 , 4 we have Output P = 6 , 8 , 10 , 12 , respectively .<br \/>\nThat is ( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 ) , ( 4 , 12 ) .<\/p>\n<p>3. Answer : ( 1 , 6 ) , ( 2 , 12 ) , ( 3 , 18 ) , ( 4 , 24 ) .<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-3.png\" alt=\"\" width=\"152\" height=\"142\" \/><br \/>\nGiven , Radius of a circle , where as\u00a0 r = 1 , 2 , 3 , 4<br \/>\nTo find the circumference of a circle , we have C = 2\u00d2r , \u00d2 = 3.14 , or we can write it as 3 .<br \/>\nfor r = 1 , C = 2 \u00d7 3 \u00d7 1 = 6 ,<br \/>\nfor r = 2 , C = 2 \u00d7 3 \u00d7 2 = 12 ,<br \/>\nfor r = 3 , C = 2 \u00d7 3 \u00d7 3 = 18 ,<br \/>\nfor r = 4 , C = 2 \u00d7 3 \u00d7 4 = 24 ,<br \/>\nSo, for every value of Input r = 1 , 2 , 3 , 4 we have Output C = 6 , 12 , 18 , 24 , respectively .<br \/>\nThat is ( 1 , 6 ) , ( 2 , 12 ) , ( 3 , 18 ) , ( 4 , 24 ) .<\/p>\n<p>4. Answer: ( 1 , 9 ) , ( 2 , 18 ) , ( 3 , 27 ) , ( 4 , 36 )<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-4.png\" alt=\"\" width=\"152\" height=\"138\" \/><br \/>\nGiven , Two Edges of a cube = 3 , h = 1 , 2 , 3 , 4<br \/>\nTo find the Volume of the cube we have , V = a\u00b3<br \/>\nfor h = 1 , V = 3 \u00d7 3 \u00d7 1 = 9 ,<br \/>\nfor h = 2 , V = 3 \u00d7 3 \u00d7 2 = 12 ,<br \/>\nfor h = 3 , V = 3 \u00d7 3 \u00d7 3 = 27 ,<br \/>\nfor h = 4 , V = 3 \u00d7 3 \u00d7 4 = 36 ,<br \/>\nSo, for every value of Input h = 1 , 2 , 3 , 4 we have Output V = 9 , 18 , 27 , 36 , respectively .<br \/>\nThat is ( 1 , 9 ) , ( 2 , 18 ) , ( 3 , 27 ) , ( 4 , 36 ) .<\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\ninput<br \/>\nmapping diagram<br \/>\nnonlinear function<br \/>\noutput<br \/>\nlinear function<\/p>\n<p>Answer : Input : The ordered pairs can be used to show inputs and outputs of a function ,The\u00a0input is the number you feed into the expression, and the output is what you get after the calculations are finished.<\/p>\n<p>mapping diagram : A relation pairs inputs with outputs , A relation can be represented by ordered pairs or a mapping diagram .<\/p>\n<p>nonlinear function : nonlinear functions are functions which are not linear. Quadratic functions are one type of nonlinear function. It is a relation between two variables , function that does not form a line when graphed.<\/p>\n<p>output ; The ordered pairs can be used to show inputs and outputs of a function ,The input is the number you feed into the expression, and the output is what you get after the calculations are finished.<\/p>\n<p>linear function : A linear function is a relation between two variables that produces a straight line when graphed. And it has one dependent variable and one independent variable .<\/p>\n<h3><a id=\"Lesson _7.1 _Relations _and _Functions\"><\/a>Lesson 7.1 Relations and Functions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Interpreting Diagrams<br \/>\nWork with a partner. Describe the relationship between the inputs and outputs in each diagram. Then complete each diagram. Is there more than one possible answer? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 1\" width=\"453\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-1.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-1-300x123.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><br \/>\nAnswer: a. The relation between the inputs and outputs is outputs are the result of twice as many times the inputs.<br \/>\nb. The relation between the inputs and outputs is outputs are the result of colors of inputs .\u00a0In this case we can notice that , for any one input we can have more than one output .<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-5.png\" alt=\"\" width=\"164\" height=\"180\" \/><br \/>\na. As shown in the diagrams , The relation between the inputs and outputs is outputs are the result of twice as many times the inputs , so for input 1 = 1 \u00d7 1 = 1 as output ,<br \/>\nfor input 2 = 2 \u00d7 2 = 4\u00a0 ,<br \/>\nfor input 3 = 3 \u00d7 3 = 9\u00a0 ,<br \/>\nfor input 5 = 5 \u00d7 5 = 25 ,<br \/>\nfor input 8 = 8 \u00d7 8 = 64 ,<br \/>\nfor input 9 = 9 \u00d7 9 = 81 ,<\/p>\n<p>So, for every value of Input = 1 , 2 , 3 , 5 , 8 , 9 , we have Output = 1 , 4 , 9 , 25 , 64 , 81 , respectively .<br \/>\nThat is ( 1 , 1 ) , ( 2 , 4 ) , ( 3 , 9 ) , ( 5 , 25 ) , ( 8 , 64 ) , ( 9 , 81 ) .<\/p>\n<p>b. The relation between the inputs and outputs is outputs are the result of colors of inputs .\u00a0<img loading=\"lazy\" class=\"alignnone size-full wp-image-46469\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-6.png\" alt=\"\" width=\"251\" height=\"151\" \/><br \/>\nfor input Blueberry = color is blue as output<br \/>\nfor\u00a0 input lemon = color is yellow as output<br \/>\nfor input Apple = color is yellow , red and green as output<br \/>\nfor input Grape = color is green as output.<\/p>\n<p>In this case we can notice that , for any one input we can have more than one output .<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Describing Relationships Between Quantities<br \/>\nWork with a partner. The diagrams show the numbers of tickets bought by customers for two different plays and the total costs (in dollars).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 2\" width=\"585\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-2.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-2-300x110.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\na. For each diagram, how many outputs does each input have?<br \/>\nb. Describe the prices of tickets for each play.<br \/>\nc. A person buys 4 tickets for each play. Can you determine the total cost of all 8 tickets? Explain.<br \/>\nAnswer:<br \/>\na. For Play A ,The number of inputs are equal to number of outputs ,<br \/>\nFor Play B , The number of inputs are not equal to number of outputs .<br \/>\nSo, input 1 = 2 outputs , input 2 = 3 outputs , input 3 = 4 outputs .<\/p>\n<p>b. For Play A , The price of the each ticket is $8 .<br \/>\nFor Play B , The price of each ticket is $4 or $8 .<\/p>\n<p>c. For Play A , each ticket is $8 , Then for 4 tickets = 4 \u00d7 $8 = $32 .<br \/>\nFor Play B , each ticket is $4 or $8 , Then for 4 tickets = 4 \u00d7 $8 = $32 . or 4 \u00d7 $4 = $16 .<\/p>\n<p>Explanation:<br \/>\na. For Play A ,<br \/>\nThe number of inputs are equal to number of outputs , 4 inputs = 4 outputs<br \/>\nThat is ( 1 , 8 ) , ( 2 , 16 ) , ( 3 , 24 ) , ( 4 , 32 ) .<br \/>\nFor Play B ,<br \/>\nThe number of inputs are not equal to number of outputs , 3 inputs are not equal to 7 outputs<br \/>\nThat is , for input 1 = 4 , 8 as outputs ,<br \/>\nfor input 2 = 8 , 12 , 16 as outputs ,<br \/>\nfor input 3 = 12 , 16 , 20 , 24 as outputs ,<br \/>\nSo, input 1 = 2 outputs , input 2 = 3 outputs , input 3 = 4 outputs .<\/p>\n<p>b. For Play A ,<br \/>\nThe price of the each ticket is $8 .<br \/>\nFor Play B ,<br \/>\nThe price of each ticket is $4 or $8 .<\/p>\n<p>c. Given , A person buys 4 tickets for each play.<br \/>\nFor Play A , each ticket is $8 , Then for 4 tickets = 4 \u00d7 $8 = $32 .<br \/>\nAnd for 8 tickets = 8 \u00d7 $8 = $64 .<br \/>\nFor Play B , each ticket is $4 or $8 , Then for 4 tickets = 4 \u00d7 $8 = $32 . or 4 \u00d7 $4 = $16 .<br \/>\nAnd for 8 tickets =8 \u00d7 $4 =$32\u00a0 or 8 \u00d7 $8 = $64 .<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 3\" width=\"182\" height=\"148\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>List the ordered pairs shown in the mapping diagram.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 4\" width=\"139\" height=\"139\" \/><br \/>\nAnswer: Ordered pairs are ( 0 , 12 ) , ( 2 , 10 ) , ( 4 , 8 ) , ( 6 , 6 ) .<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 0 , 12 ) , ( 2 , 10 ) , ( 4 , 8 ) , ( 6 , 6 ) .<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 5\" width=\"156\" height=\"127\" \/><br \/>\nAnswer: Ordered pairs are ( 1 , -1 ) , ( 1 , -2 ) , ( 2 , -3 ) , ( 2 , -4 ) .<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 1 , -1 ) , ( 1 , -2 ) , ( 2 , -3 ) , ( 2 , -4 ) .<\/p>\n<p><strong>Determine whether the relation is a function.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 6\" width=\"151\" height=\"135\" \/><br \/>\nAnswer: The relation is not a function<\/p>\n<p>Explanation:<br \/>\nThe each input has\u00a0 more than two outputs , Even one of those inputs are unclear of outputs<br \/>\nSo , The relation is not a function .<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 7\" width=\"149\" height=\"137\" \/><br \/>\nAnswer: The relation is a function .<\/p>\n<p>Explanation:<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>PRECISION<\/strong><br \/>\nDescribe how relations and functions are different.<br \/>\nAnswer: Relations are nothing but the ordered pairs with Inputs and Outputs . On the other hand , Functions are The relation that pairs with one input with exactly one output\u00a0 are called Functions.<\/p>\n<p><strong>IDENTIFYING FUNCTIONS<\/strong> List the ordered pairs shown in the mapping diagram. Then determine whether the relation is a function.<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 8\" width=\"147\" height=\"136\" \/><br \/>\nAnswer: The ordered pairs are ( 10 , 1 ) , ( 15 , 1 ) , ( 20 , 13 ) , ( 25 , 7 ) and The relation is a function .<\/p>\n<p>Explanation:<br \/>\nAs shown , The ordered pairs are ( 10 , 1 ) , ( 15 , 1 ) , ( 20 , 13 ) , ( 25 , 7 ) .<br \/>\nEach input has exactly one output ,<br \/>\nSo, The relation is a function .<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 9\" width=\"146\" height=\"136\" \/><br \/>\nAnswer: The ordered pairs are ( 0 , -5 ) , ( 0 , -4 ) , ( 1 , -4 ) , ( 2 , -3 ) , ( 3 , -2 ) and relation is not a function .<\/p>\n<p>Explanation:<br \/>\nAs shown , The ordered pairs are ( 0 , -5 ) , ( 0 , -4 ) , ( 1 , -4 ) , ( 2 , -3 ) , ( 3 , -2 ) .<br \/>\nThe input 0 has more than one output ,<br \/>\nSo, The relation is not a function .<\/p>\n<p>Question 8.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nCopy and complete the mapping diagram at the left to represent a relation that is a function. Then describe how you can not modify the mapping diagram so that the relation is a function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 10\" width=\"166\" height=\"142\" \/><br \/>\nAnswer: ordered pairs are ( -8 , -4 ) , ( 0 , -2 ) , ( 8 , 0 ) , ( 16 , 2 ) . To have the relation as a function we must have only one output for one input.<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.png\" alt=\"\" width=\"148\" height=\"130\" \/><br \/>\nThe ordered pairs of the diagram are ( -8 , -4 ) , ( 0 , -2 ) , ( 8 , 0 ) , ( 16 , 2 ) .<br \/>\nEach Input must have only one output in order to be the relation is a function ,<br \/>\nIf ,The mapping diagram has the right to left representation or each input has more than one output , then the relation is not a function .<br \/>\nSo , To have the relation as a function we must have only one output for one input.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 9.<br \/>\nThe mapping diagram represents the costs of reserving a hotel room for different numbers of nights.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 11\" width=\"143\" height=\"154\" \/><br \/>\na. Is the cost a function of the number of nights reserved?<br \/>\nb. Describe the relationship between the cost and the number of nights reserved.<br \/>\nAnswer: a. Yes , The cost is a function of the number of nights reserved .<br \/>\nb. The relationship between the cost and the number of nights reserved is , For every night reservation of the room is increasing by $85 with increase in the next reservation ,<\/p>\n<p>Explanation:<br \/>\na. From the diagram we have ,<br \/>\nOrdered pairs are ( 1 , -$85 ) , ( 2 , $170 ) , ( 3 , $255 ) , ( 4 , $340 ) . each input has exactly one output ,<br \/>\nSo , the relation is a function and ,<br \/>\nYes , The cost is a function of the number of nights reserved .<\/p>\n<p>b. The relationship between the cost and the number of nights reserved is ,<br \/>\nFor every night reservation of the room is increasing by $85 with increase in the next reservation,<br \/>\nthat is , input 1 = $85 as output<br \/>\nInput 2 = $85 + $85 = $170 as output<br \/>\nInput 3 = $170 + $85 = $255 as output<br \/>\nInput 2 = $255 + $85 = $340 as output<\/p>\n<p>So, The relationship between the cost and the number of nights reserved is ,<br \/>\nFor every night reservation of the room is increasing by $85 with increase in the next reservation.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe graph represents the number of contestants in each round of a talent competition.<br \/>\na. Is the number of contestants a function of the round number?<br \/>\nb. Predict the number of contestants in the talent competition during Round 7. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 12\" width=\"161\" height=\"247\" \/><br \/>\nAnswer: a. The number of contestants is a function of the round number.<br \/>\nb. The number of contestants in the talent competition during Round 7\u00a0 are 2.<\/p>\n<p>Explanation:<br \/>\na. From the given graph , The ordered pairs are ( 1 , 128 ) , ( 2 , 64 ) , ( 3 , 32 ) , ( 4 , 16 ) .<br \/>\nEach input has only one output , The relation is a function .<br \/>\nSo , the number of contestants is a function of the round number.<\/p>\n<p>b. Firstly , The relation between the input and output is,<br \/>\nWith every increase in the round number the number of contestants are decreasing by half the number of the previous round , That is, for\u00a0 input 1 = 128 as output<br \/>\nFor input 2 = 128 &#8211; 64 = 64\u00a0 as output<br \/>\nFor input 3 = 64 &#8211; 32 = 32\u00a0 as output<br \/>\nFor input 4 = 32 &#8211; 16 = 16\u00a0 as output<br \/>\nFor input 5 = 16 &#8211; 8 = 8\u00a0 as output<br \/>\nFor input 6 = 8 &#8211; 4 = 4\u00a0 as output<br \/>\nFor input 7 = 4 &#8211; 2 = 2\u00a0 as output,<br \/>\nSo, The\u00a0number of contestants in the talent competition during Round 7\u00a0 are 2 .<\/p>\n<h3><a id=\"Relations _and _Functions _Homework _&amp; _Practice _7.1\"><\/a>Relations and Functions Homework &amp; Practice 7.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Choose an appropriate data display for the situation. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\nthe number of runners in each<br \/>\nage group at a marathon<br \/>\nAnswer: In a marathon ,the people of all age group are participating for a promotion on healthy lifestyle, The number of runners in each\u00a0 group has kids, adults and old people to spread the awareness of leading a healthy life by running daily in the morning . Running or jogging in the morning can help us to maintain our body mass index at an optimal level which is good for heart. The Marathon is conducted by the government of health ministry to be example for the future generations.<\/p>\n<p>Question 2.<br \/>\nthe high temperature and the<br \/>\nattendance at a water park each day<br \/>\nAnswer:\u00a0 Generally, The water park is normally crowded depending on the season and the temperature, In summer the attendance in the waterpark is at the utmost point because of the high temperature and the seasonal vacation. Going to the water park in summer is super fun due to the number of\u00a0 water slides , water rides will be a nice place to the whole family trip and as well as friends . In order to be there at a less crowded time spring is also a nice time to visit the water park .<\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 3.<br \/>\ny = 2x &#8211; 3<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-8.png\" alt=\"\" width=\"541\" height=\"426\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-8.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-8-300x236.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\nExplanation:<br \/>\nGiven , y = 2x \u2013 3 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 1 , then y = 2(1) \u2013 3 = 2 &#8211; 3 = -1 . co-ordinates are (1 , -1)<br \/>\nif x = 2 , then y = 2(2) \u2013 3 = 4 &#8211; 3 = 1 , co-ordinates are (2 , 1)<br \/>\nThe co-ordinates (1 , -1) , (2 , 1) form a straight line .<br \/>\nSo, y = 2x \u2013 3 is a linear equation.<\/p>\n<p>Question 4.<br \/>\ny = &#8211; 0.5x<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-9.png\" alt=\"\" width=\"538\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-9.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-9-300x236.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><br \/>\nExplanation:<br \/>\nGiven , y = -0.5x , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = -0.5(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 2 , then y = -0.5(2) = -1 , co-ordinates are (2 , -1)<br \/>\nThe co-ordinates (0 , 0) , (2 , -1) form a straight line .<br \/>\nSo, y = -0.5x is a linear equation.<\/p>\n<p>Question 5.<br \/>\ny = &#8211; 3x + 4<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-46952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-10.png\" alt=\"\" width=\"544\" height=\"422\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-10.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-10-300x233.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\nExplanation:<br \/>\nGiven , y = \u2013 3x + 4 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = \u2013 3(0) + 4 = 4 . co-ordinates are (0 , 4)<br \/>\nif x = 1 , then y = \u2013 3(1) + 4 = -3 + 4 = 1 , co-ordinates are (1 , 1)<br \/>\nif x = 2 , then y = \u2013 3(2) + 4 = -6 + 4 = -2 , co-ordinates are (2 , -2)<br \/>\nThe co-ordinates (0 , 4) , (1 , 1) , (2 , -2) form a straight line .<br \/>\nSo, y = \u2013 3x + 4 is a linear equation.<\/p>\n<p>Question 6.<br \/>\nWhich word best describes two figures that have the same size and the same shape?<br \/>\nA. congruent<br \/>\nB. adjacent<br \/>\nC. parallel<br \/>\nD. similar<br \/>\nAnswer:\u00a0 A. congruent<\/p>\n<p>Explanation:<br \/>\nTwo figures which have the same size and shape are congruent.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>INTERPRETING DIAGRAMS<\/strong> Describe the relationship between the inputs and outputs in the diagram. Then complete the diagram. Is there more than one possible answer? Explain your reasoning. (See Exploration 1, p. 275.)<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 13\" width=\"146\" height=\"172\" \/><br \/>\nAnswer: The relationship between the inputs and outputs in the diagram is ,<br \/>\nFor every increase in number of input is having the output of adding -4 to the previous output.<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-47915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-11.png\" alt=\"\" width=\"154\" height=\"171\" \/><br \/>\nThe relationship between the inputs and outputs in the diagram is ,<br \/>\nFor every increase in number of input is having the output of adding -4 to the previous output ,<br \/>\nfor input 1 = -1 as output<br \/>\nfor input 2 = -1 + (-4) = -5 as output<br \/>\nfor input 3 = -5 + (-4) = -9 as output<br \/>\nfor input 4 = -9 + (-4) = -13 as output<br \/>\nfor input 5 = -13 + (-4) = -17 as output<br \/>\nfor input 6 = -17 + (-4) = -21 as output.<br \/>\nSo, The relationship between the inputs and outputs in the diagram is ,<br \/>\nFor every increase in number of input is having the output of adding -4 to the previous output .<\/p>\n<p>In this case , we are witnessing only one output for one input.<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 14\" width=\"205\" height=\"161\" \/><br \/>\nAnswer: The relationship between the inputs and outputs in the diagram is,<br \/>\nEach input has the sports name and the output has the Starting letter of sports name.<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-47918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-12.png\" alt=\"\" width=\"204\" height=\"152\" \/><br \/>\nThe relationship between the inputs and outputs in the diagram is,<br \/>\nEach input has the sports name and the output has the Starting letter of sports name.<br \/>\nFor input basketball = b as output<br \/>\nFor input baseball = b as output<br \/>\nFor input football = f as output<br \/>\nFor input soccer = s as output<br \/>\nFor input swimming = s as output,<br \/>\nSo, The relationship between the inputs and outputs in the diagram is,<br \/>\nEach input has the sports name and the output has the Starting letter of sports name.<\/p>\n<p>In this case we have more than one output for input.<\/p>\n<p><strong>LISTING ORDERED PAIRS<\/strong> List the ordered pairs shown in the mapping diagram.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 15\" width=\"145\" height=\"127\" \/><br \/>\nAnswer: Ordered pairs are ( 0 , 4 ) , ( 3 , 5 ) , ( 6 , 6 ) , ( 9 , 7 ) .<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 0 , 4 ) , ( 3 , 5 ) , ( 6 , 6 ) , ( 9 , 7 ) .<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 16\" width=\"142\" height=\"128\" \/><br \/>\nAnswer: Ordered pairs are ( 1 , 8 ) , ( 3 , 8 ) , ( 3 , 4 ) , ( 5 , 6 ) , ( 7 , 2 ).<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 1 , 8 ) , ( 3 , 8 ) , ( 3 , 4 ) , ( 5 , 6 ) , ( 7 , 2 ).<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 17\" width=\"173\" height=\"130\" \/><br \/>\nAnswer: Ordered pairs are ( 6 , -5 ) , ( 7 , -5 ) , ( 8 , -10 ) , ( 9 , -10 ).<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 6 , -5 ) , ( 7 , -5 ) , ( 8 , -10 ) , ( 9 , -10 ).<\/p>\n<p><strong>IDENTIFYING FUNCTIONS<\/strong> Determine whether the relation is a function.<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 18\" width=\"146\" height=\"139\" \/><br \/>\nAnswer: The relation is not a function .<\/p>\n<p>Explanation:<br \/>\nThe each input has\u00a0 more than two outputs , That is one input has multiple number of outputs.<br \/>\nHere , input 0 has two outputs which are 10 and 20 .<br \/>\nSo , The relation is not a function .<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 19\" width=\"153\" height=\"141\" \/><br \/>\nAnswer: The relation is a function .<\/p>\n<p>Explanation:<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 20\" width=\"163\" height=\"139\" \/><br \/>\nAnswer: The relation is a function .<\/p>\n<p>Explanation:<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend determines whether the relation shown in the mapping diagram is a function. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 21\" width=\"322\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-21.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-21-300x150.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer: The relation is not a function .<\/p>\n<p>Explanation:<br \/>\nThe each input has\u00a0 more than two outputs , That is one input has multiple number of outputs.<br \/>\nHere , input 4 has four outputs which are 5, 6 , 7 and 8.<br \/>\nSo , The relation is not a function .<\/p>\n<p><strong>REASONING<\/strong> Draw a mapping diagram that represents the relation. Then determine whether the relation is a function. Explain.<br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-22.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 22\" width=\"148\" height=\"146\" \/><br \/>\nAnswer:\u00a0 The mapping diagram representing the relation is <img loading=\"lazy\" class=\"alignnone size-full wp-image-47965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-13.png\" alt=\"\" width=\"144\" height=\"134\" \/><\/p>\n<p>Explanation:<br \/>\nFrom the given graph , co-ordinates of the ordering pairs are( 1 , 1 ), ( 3 , 3 ), ( -1 , -1 ), ( -3 , -3 ).<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-23.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 23\" width=\"143\" height=\"147\" \/><br \/>\nAnswer: The mapping diagram representing the relation is <img loading=\"lazy\" class=\"alignnone size-full wp-image-47985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-15.png\" alt=\"\" width=\"203\" height=\"198\" \/><\/p>\n<p>Explanation:<br \/>\nFrom the given graph , co-ordinates of the ordering pairs are( 0 , 8 ),( 2 , 8 ),( 4 , 8 ),( 6 , 8 ),( 8 , 8 ),( -2 , 8 ),( -4 , 8 ). Each input has exactly one output ,<br \/>\nSo , The relation is a function.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-24.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 24\" width=\"140\" height=\"139\" \/><br \/>\nAnswer: The mapping diagram representing the relation is <img loading=\"lazy\" class=\"alignnone size-full wp-image-47986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-14.png\" alt=\"\" width=\"175\" height=\"187\" \/><\/p>\n<p>Explanation:<br \/>\nFrom the given graph , co-ordinates of the ordering pairs are( -2 , 1 ),( -2 , 2 ),( -2 , 3 ),( -2 , 4 ),( -2 , 5 ),( -2 , 6 ).<br \/>\nEach input has more than one output ,<br \/>\nSo , The relation is not a function.<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe normal pressure at sea level is 1 atmosphere of pressure(1 ATM). As you dive below sea level, the pressure changes. The mapping diagram represents the pressures at different depths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-25.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 25\" width=\"338\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-25.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-25-300x275.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><br \/>\na. Complete the mapping diagram.<br \/>\nb. Is pressure a function of depth?<br \/>\nc. Describe the relationship between pressure and depth.<br \/>\nd. List the ordered pairs. Then plot the ordered pairs in a coordinate plane. What do you notice about the points?<br \/>\ne. RESEARCH What are common depths for beginner scuba divers? What are common depths for experienced scuba divers?<br \/>\nAnswer: The detailed explanation of\u00a0 all the answers are given below .<\/p>\n<p>Explanation:<br \/>\na. The mapping diagram is <img loading=\"lazy\" class=\"alignnone size-full wp-image-48167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-16.png\" alt=\"\" width=\"195\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-16.png 195w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-16-150x150.png 150w\" sizes=\"(max-width: 195px) 100vw, 195px\" \/><br \/>\nb. Yes , the pressure is a function of depth, Because depth is related to pressure in the given mapping diagram.<\/p>\n<p>c. The relationship between pressure and depth is,<br \/>\nfor every 10m increase in Depth of input there is an increase in 1 ATM pressure .<\/p>\n<p>d. The ordered pairs are ( 0 , 1 ) , ( 10 , 2 ) , (20 , 3 ) , ( 30 , 4 ) , ( 40 , 5 ), ( 50 , 6 ).<br \/>\nThe plot of the ordered pairs in a coordinate plane is <img loading=\"lazy\" class=\"alignnone size-full wp-image-48324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-17.png\" alt=\"\" width=\"487\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-17.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Function-17-300x264.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>From the graph, we have seen that, if the depth of the diving of scuba drivers increases then the water pressure increases with increase in depth. So, the graph have straight line .<\/p>\n<p>e. The common depths for beginner scuba divers is 30 feet to 60 feet or 9 to 18 meters ,<br \/>\nThe common depths for experienced scuba divers is more than 60 feet or more than 18 meters .<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the cost of purchasing 1, 2, 3, or 4 T-shirts from a souvenir shop.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-26.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 26\" width=\"143\" height=\"135\" \/><br \/>\na. Is the cost a function of the number of T-shirts purchased?<br \/>\nb. Describe the relationship between the cost and the number cost per T-shirt of T-shirts purchased. How does the change as you purchase more T-shirts?<br \/>\nAnswer: The detailed explanation of\u00a0 all the answers are given below .<\/p>\n<p>Explanation:<br \/>\na. Yes , The cost is a function of the number of T-shirts purchased, Because the cost of the purchased T-shirts is varying with the number of T-shirts purchased.<\/p>\n<p>b. The relationship between the cost and the number cost per T-shirt of T-shirts purchased is,<br \/>\nInput is the cost of 1 T-shirt is $10 as output , Then for 2 T-shirts cost will be $20<br \/>\nIf 2 T-shirts will be purchased at same time, cost will be decreased by $2 so it will be $10 + 8 = $18 for 2 T-shirts.<br \/>\nAs per the single T-shirt cost , For 3 T-shirts will be $30,<br \/>\nSo in the table given that 3 T-shirts will cost $24 , because it cost $18 + 6 = $24 for 3 T-shirts.<br \/>\nIt goes same for 4 T-shirts , For 4 T-shirts will be $40, because it cost $24 + 4 = $28 for 4 T-shirts.<\/p>\n<p>The change as you purchase more T-shirts is For every increase in purchase of the number of T-shirts is decrease in the cost of total T-shirts purchased.<\/p>\n<p>Question 21.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nThe table shows the outputs for several inputs. Use two methods to predict the output for an input of 200.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.1-27.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.1 27\" width=\"252\" height=\"71\" \/><br \/>\nAnswer: The output for an input of 200 is 1025.<\/p>\n<p>Explanation:<br \/>\nMethod 1. The relation between inputs and outputs is as follows,<br \/>\ny = 25 + 5x<br \/>\nAs input increases by 1 , output increases by 5 units,<br \/>\nTo find output of 200 as input ,<br \/>\nput x = 200 in the equation,<br \/>\ny = 25 + 5(200)<br \/>\n= 25 + 1000<br \/>\n= 1025.<br \/>\nSo , y = 1025.<\/p>\n<p>Method 2.\u00a0 As the table shown, for every increase in input there is an increase in 5 numbers in output,<br \/>\nSo , For 1 input = 25 + 5 = 30 as output<br \/>\nFor 2 input = 30 + 5 = 35 as out put<br \/>\nFor 3 input = 35 + 5 = 40 as out put<br \/>\nFor 4 input = 40 + 5 = 45 as out put<br \/>\nBy doing this for number 200 as input we have , 1025 as output.<\/p>\n<h3><a id=\"Lesson _7.2 _Representations _of _Functions\"><\/a>Lesson 7.2 Representations of Functions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Table to Describe Relationships<br \/>\nWork with a partner. Make a table that shows the relationship\u00a0 between the figure number x and the area A of each figure. Then use an equation to find which figure has an area of 81 square units when the pattern continues.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 1\" width=\"539\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-1.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-1-300x126.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Answer: a. The equation is y = 2x &#8211; 1, For figure has an area of 81 square units is 41.<br \/>\nb. The equation is y = x\u00b2,\u00a0 For figure has an area of 81 square units is 9.<\/p>\n<p>Explanation:<br \/>\na. figure shows the 1 square unit of each box\u00a0 for and it has a pattern of\u00a0 2x &#8211; 1<br \/>\nfigure 1 = 1 square unit<br \/>\nfigure 2 =3 square units<br \/>\nfigure 3 = 5 square unit and so on<br \/>\nSo, the equation is y = 2x &#8211; 1 , it is in the form of y = mx + c,<br \/>\nGiven to which figure has an area of 81 square units<br \/>\nsubstitute y\u00a0 = 81, we have<br \/>\ny = 2x &#8211; 1<br \/>\n81 = 2x &#8211; 1<br \/>\n2x = 82<br \/>\nx = 41<br \/>\nSo, For figure has an area of 81 square units is 41.<\/p>\n<p>b. As shown above , we know that ,<br \/>\nfigure 1 = 1 square unit<br \/>\nfigure 2 =4 square units<br \/>\nfigure 3 = 9 square unit and so on<br \/>\nHere we have a pattern of power of its own number,<br \/>\nSo, the Equation\u00a0 will be y = x\u00b2<br \/>\nGiven to which figure has an area of 81 square units<br \/>\nsubstitute y\u00a0 = 81, we have<br \/>\nx\u00a0 = 9<br \/>\nSo, For figure has an area of 81 square units is 9.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using a Graph<br \/>\nWork with a partner. Use a graph to test the truth of each statement. If the statement is true, write an equation that shows how to obtain one measurement from the other.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 2\" width=\"391\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-2.png 391w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-2-300x150.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><br \/>\na. \u201cYou can find the horsepower of a race-car car engine if you know its volume in cubic inches&#8221;<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 3\" width=\"395\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-3.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-3-300x49.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><br \/>\nb. \u201cYou can find the volume of a race-car engine in cubic centimeters if you know its volume in cubic inches.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 4\" width=\"385\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-4.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-4-300x56.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Answer: a. Given ordered pairs are (200 , 375) , (350 , 650) , (350 , 250) , (500 , 600)<br \/>\nWe can not find the horsepower of a race-car car engine if you know its volume in cubic inches<br \/>\nb. Given ordered pairs are (100 , 1640) , (200 , 3280) , (300 , 4920) ,<br \/>\nYes, You can find the volume of a race-car engine in cubic centimeters if you know its volume in cubic inches<\/p>\n<p>Explanation:<br \/>\na. Given ordered pairs are (200 , 375) , (350 , 650) , (350 , 250) , (500 , 600)<br \/>\nWe can not find the horsepower of a race-car car engine if you know its volume in cubic inches<\/p>\n<p>b. Given ordered pairs are (100 , 1640) , (200 , 3280) , (300 , 4920) ,<br \/>\nYes, You can find the volume of a race-car engine in cubic centimeters if you know its volume in cubic inches<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 5\" width=\"188\" height=\"71\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nWrite a function rule for \u201cThe output is one-fourth of the input.\u201d<br \/>\nAnswer:\u00a0 y = \\(\\frac{x}{4}\\)<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is one-fourth of the input, will be ,<br \/>\ny = \\(\\frac{x}{4}\\).<\/p>\n<p><strong>Find the value of y when x = 5.<\/strong><br \/>\nQuestion 2.<br \/>\ny = 4x &#8211; 1<br \/>\nAnswer: y = 19.<\/p>\n<p>Explanation:<br \/>\nGiven, y = 4x &#8211; 1<br \/>\nsubstitute x = 5 , we get<br \/>\ny = 4(5) &#8211; 1<br \/>\ny = 20 &#8211; 1 = 19<br \/>\nSo, y = 19.<\/p>\n<p>Question 3.<br \/>\ny = 10x<br \/>\nAnswer: y = 50<\/p>\n<p>Explanation:<br \/>\nGiven, y =10x<br \/>\nsubstitute x = 5 , we get<br \/>\ny = 10(5)<br \/>\ny = 50<br \/>\nSo, y = 50.<\/p>\n<p>Question 4.<br \/>\ny = 7 &#8211; 3x<br \/>\nAnswer: y = -8.<\/p>\n<p>Explanation:<br \/>\nGiven, y = 7 &#8211; 3x<br \/>\nsubstitute x = 5 , we get<br \/>\ny = 7 &#8211; 3(5)<br \/>\ny = 7 &#8211; 15 = -8<br \/>\nSo, y = -8.<\/p>\n<p><strong>Graph the function.<\/strong><br \/>\nQuestion 5.<br \/>\ny = x + 1<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-18.png\" alt=\"\" width=\"445\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-18.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-18-300x259.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = x + 1 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 + 1 = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = 1 + 1 = 2 . co-ordinates are (1 , 2)<br \/>\nif x = 2 , then y = 2 + 1 = 3 , co-ordinates are (2 , 3)<br \/>\nThe co-ordinates (0 , 1) , (1 , 2) , (2 , 3) form a straight line .<\/p>\n<p>Question 6.<br \/>\ny = &#8211; 3x<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-20.png\" alt=\"\" width=\"504\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-20.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-20-300x219.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; 3x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = -3(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = -3(1) = -3 . co-ordinates are (1 , -3)<br \/>\nif x = 2 , then y = -3(2) = -6 , co-ordinates are (2 , -6)<br \/>\nif x = 3 , then y = -3(3) = -9 , co-ordinates are (3 , -9)<br \/>\nThe co-ordinates (0 , 0) , (1 , -3) , (2 , -6) ,(3 , -9) form a straight line .<\/p>\n<p>Question 7.<br \/>\ny = 3x + 2<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-19.png\" alt=\"\" width=\"443\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-19.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-19-300x260.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = 3x + 2 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =3(0) + 2 = 2 . co-ordinates are (0 , 2)<br \/>\nif x = 1 , then y = 3(1) + 2= 5 . co-ordinates are (1 , 5)<br \/>\nif x = 2 , then y =3(2) + 2 = 7 , co-ordinates are (2 , 7)<br \/>\nThe co-ordinates (0 , 2) , (1 , 5) , (2 , 7) form a straight line .<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>WRITING FUNCTION RULES<\/strong> Write a function rule for the statement.<br \/>\nQuestion 8.<br \/>\nThe output is three times the input.<br \/>\nAnswer: y = 3x<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is three times the input. will be ,<br \/>\nSo , y = 3x .<\/p>\n<p>Question 9.<br \/>\nThe output is eight more than one-seventh of the input.<br \/>\nAnswer: y = 8 + \\(\\frac{x}{7}\\) .<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is eight more than one-seventh of the input., will be ,<br \/>\nSo, y = 8 + \\(\\frac{x}{7}\\) .<\/p>\n<p><strong>EVALUATING A FUNCTION<\/strong> Find the value of y when x = 5.<br \/>\nQuestion 10.<br \/>\ny = 6x<br \/>\nAnswer: y = 30<\/p>\n<p>Explanation:<br \/>\nGiven, y = 6x<br \/>\nsubstitute x = 5 , we get<br \/>\ny = 6(5) =30<br \/>\nSo, y = 30<\/p>\n<p>Question 11.<br \/>\ny = 11 &#8211; x<br \/>\nAnswer: y = 6<\/p>\n<p>Explanation:<br \/>\nGiven, y = 11 &#8211; x<br \/>\nsubstitute x = 5 , we get<br \/>\ny = 11 &#8211; 5 = 6<br \/>\nSo, y = 6.<\/p>\n<p>Question 12.<br \/>\ny = \\(\\frac{1}{5}\\)x + 1<br \/>\nAnswer:\u00a0 y = 2.<\/p>\n<p>Explanation:<br \/>\nGiven, y = \\(\\frac{1}{5}\\)x + 1<br \/>\nsubstitute x = 5 , we get<br \/>\ny = \\(\\frac{x}{5}\\) + 1<br \/>\ny= \\(\\frac{5}{5}\\) + 1<br \/>\ny = 1 + 1 = 2<br \/>\nSo, y = 2 .<\/p>\n<p><strong>GRAPHING A FUNCTION<\/strong> Graph the function.<br \/>\nQuestion 13.<br \/>\ny = &#8211; 2x<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-22.png\" alt=\"\" width=\"499\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-22.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-22-300x218.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; 2x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = &#8211; 2(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = &#8211; 2(1)= -2 . co-ordinates are (1 , -2)<br \/>\nif x = 2 , then y =- 2(2) = -4 , co-ordinates are (2 , -4)<br \/>\nif x = 3 , then y =- 2(3) = -6 , co-ordinates are (3 , -6)<br \/>\nThe co-ordinates (0 , 0) , (1 , -2) , (2 , -4) , (3 , -6) form a straight line .<\/p>\n<p>Question 14.<br \/>\ny = x &#8211; 3<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-23.png\" alt=\"\" width=\"501\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-23.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-23-300x217.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = x &#8211; 3 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 &#8211; 3 = -3 . co-ordinates are (0 , -3)<br \/>\nif x = 1 , then y = 1\u00a0&#8211; 3= -2 . co-ordinates are (1 , -2)<br \/>\nif x = 2 , then y = 2 &#8211; 3 = -1 , co-ordinates are (2 , -1)<br \/>\nif x = 3 , then y = 3 &#8211; 3 = 0 , co-ordinates are (3 , 0)<br \/>\nThe co-ordinates (0 , -3) , (1 , -2) , (2 , -1) , (3 , 0) form a straight line .<\/p>\n<p>Question 15.<br \/>\ny = 9 &#8211; 3x<br \/>\nAnswer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-49928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-21.png\" alt=\"\" width=\"500\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-21.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-21-300x219.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = 9 &#8211; 3x , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 9 &#8211; 3(0) = 9 . co-ordinates are (0 , 9)<br \/>\nif x = 1 , then y = 9 &#8211; 3(1) = 6 . co-ordinates are (1 , 6)<br \/>\nif x = 2 , then y = 9 &#8211; 3(2) = 3 , co-ordinates are (2 , 3)<br \/>\nif x = 3 , then y = 9 &#8211; 3(3) = 0 , co-ordinates are (3 , 0)<br \/>\nThe co-ordinates (0 , 9) , (1 , 6) , (2 , 3) , (3 , 0) form a straight line .<\/p>\n<p>Question 16.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 6\" width=\"424\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-6.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-6-300x87.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><br \/>\nAnswer: As mentioned in the explanation below\u00a0 a &amp; d , b &amp; c are different .<\/p>\n<p>Explanation:<br \/>\nGiven ,<br \/>\na. what output is 4 more than twice the input 3?<br \/>\nLet us say that , y is output and x is input and given as 3 ,<br \/>\nthen, we have y = 4 + 2(3) = 10.<br \/>\nb. What output is twice the sum of the input 3 and 4?<br \/>\nLet us say that , y is output and x is input and given as 3 ,<br \/>\nthen, we have y = 2( 3 + 4 ) = 14.<br \/>\nc. what output is the sum of 2 times the input 3 and 4?<br \/>\nLet us say that , y is output and x is input and given as 3 ,<br \/>\nthen, we have y = 2( 3 + 4 ) = 14.<br \/>\nd. what output is 4 increased by twice the input 3?<br \/>\nLet us say that , y is output and x is input and given as 3 ,<br \/>\nthen, we have y = 4 + 2(3) = 10.<\/p>\n<p>So, a &amp; d , b &amp; c are different .<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 17.<br \/>\nThe World Health Organization(WHO) suggests having 23 health-care workers for every 10,000 people. How many health-care workers are needed to meet the WHO suggestion for a population of 250,000 people? Justify your answer using a graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 7\" width=\"162\" height=\"257\" \/><br \/>\nAnswer: So, 575 health-care workers are needed to meet the WHO suggestion for a population of 250,000 people<\/p>\n<p>Explanation:<br \/>\nGiven, The World Health Organization(WHO) suggests having 23 health-care workers for every 10,000 people.<br \/>\nwe need to find how many health-care workers are needed to meet the WHO suggestion for a population of 250,000 people,<br \/>\nFor every 10,000 people we have 23 care takers<br \/>\nThen for 250,000 people we have<br \/>\n\\(\\frac{23 \u00d7 250,000}{10,000}\\)<br \/>\n= 23 \u00d7 25<br \/>\n= 575<br \/>\nSo, 575 health-care workers are needed to meet the WHO suggestion for a population of 250,000 people<\/p>\n<p>Question 18.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA truck produces 22 pounds of carbon dioxide for every gallon of diesel fuel burned. The fuel economy of the truck is 18 miles per gallon. Write and graph a function that describes the relationship between carbon dioxide produced and distance traveled.<br \/>\nAnswer: y = 22x + 18\u00a0 is the linear equation<\/p>\n<p>Explanation:<br \/>\nGiven, A truck produces 22 pounds of carbon dioxide for every gallon of diesel fuel burned.<br \/>\nThe fuel economy of the truck is 18 miles per gallon.<br \/>\nSo, we have y = 22x + 18 is in the form of y = mx +c<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 22(0) + 18 = 18 . co-ordinates are (0 , 18)<br \/>\nif x = 1 , then y =22(1) + 18= 40\u00a0 . co-ordinates are (1 , 40)<br \/>\nif x = 2 , then y =22(2) + 18 = 62 , co-ordinates are (2 , 62)<br \/>\nif x = 3 , then y =22(3) + 18 = 84\u00a0 , co-ordinates are (3 , 84)<br \/>\nThe co-ordinates (0 , 18) , (1 , 40) , (2 , 62) , (3 , 84) form a straight line .<br \/>\nThe graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-74.png\" alt=\"\" width=\"431\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-74.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-74-300x258.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<h3><a id=\"Representations _of _Functions _Homework _&amp; _Practice _7.2\"><\/a>Representations of Functions Homework &amp; Practice 7.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Determine whether the relation is a function.\u00a0<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 8\" width=\"140\" height=\"129\" \/><br \/>\nAnswer:\u00a0 The relation is a function .<\/p>\n<p>Explanation:<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 9\" width=\"149\" height=\"133\" \/><br \/>\nAnswer:\u00a0 The relation is a function .<\/p>\n<p>Explanation:<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 10\" width=\"142\" height=\"144\" \/><br \/>\nAnswer: The relation is not a function .<\/p>\n<p>Explanation:<br \/>\nThe each input has\u00a0 more than two outputs , That is one input has multiple number of outputs.<br \/>\nHere , input 2 has two outputs which are 0 and -4 .<br \/>\nSo , The relation is not a function .<\/p>\n<p><strong>Find the slope of the line.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 11\" width=\"153\" height=\"147\" \/><br \/>\nAnswer: slope = 1.<\/p>\n<p>Explanation:<br \/>\nBy using the slope equation , we know that<br \/>\nSlope = \\(\\frac{change in y}{change in x}\\) or<br \/>\nslope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nFrom the graph we know that change in y or \u25b2y is change from -2 to -4 =2<br \/>\nchange in x or \u25b2x is change from 1 to 3 = 2 ,<br \/>\nSo, slope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nslope = \\(\\frac{2}{2}\\)<br \/>\nslope = 1.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 12\" width=\"151\" height=\"146\" \/><br \/>\nAnswer: slope = \\(\\frac{5}{2}\\) .<\/p>\n<p>Explanation:<br \/>\nBy using the slope equation , we know that<br \/>\nSlope = \\(\\frac{change in y}{change in x}\\) or<br \/>\nslope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nFrom the graph we know that change in y or \u25b2y is change from -4 to 1 = 5<br \/>\nchange in x or \u25b2x is change from -1 to -3 = 2 ,<br \/>\nSo, slope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nslope = \\(\\frac{5}{2}\\) .<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 13\" width=\"140\" height=\"142\" \/><br \/>\nAnswer:\u00a0 slope = \\(\\frac{1}{3}\\) .<\/p>\n<p>Explanation:<br \/>\nBy using the slope equation , we know that<br \/>\nSlope = \\(\\frac{change in y}{change in x}\\) or<br \/>\nslope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nFrom the graph we know that change in y or \u25b2y is change from -4 to -3 = 1<br \/>\nchange in x or \u25b2x is change from 1 to 4 = 3 ,<br \/>\nSo, slope = \\(\\frac{\u25b2y}{\u25b2x}\\)<br \/>\nslope = \\(\\frac{1}{3}\\) .<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A GRAPH<\/strong> Use a graph to test the truth of the statement. If the statement is true, write an equation that shows how to obtain one measurement from the other measurement. (See Exploration 2, p. 281.)<\/p>\n<p>Question 7.<br \/>\n\u201cYou can find the weight of a cell phone in ounces if you know its screen size in inches.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 14\" width=\"381\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-14.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-14-300x48.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\nAnswer: we can does not find the weight of a cell phone in ounces if you know its screen size in inches.<\/p>\n<p>From the given table , Ordered pairs are (4 , 4) , (4.7 , 4.8) , (5 , 4.8) , (5.5 , 6.4)<br \/>\nFirst find the slope m of the line containing the two given points (4, 4) and (4.7, 4.8)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (4.8 \u2013 4) \/ (4.7 \u2013 4)<br \/>\nm = 0.8\/0.7 .<br \/>\nSo, we can does not find the weight of a cell phone in ounces if you know its screen size in inches.<\/p>\n<p>Question 8.<br \/>\n\u201cYou can find the age of a child in years if you know the age of the child in months.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 15\" width=\"352\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-15.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-15-300x62.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nAnswer: YES, y = 0.08x + 0.04 is a linear equations<\/p>\n<p>Explanation:<br \/>\nFrom the given table , Ordered pairs are (9 , 0.75) , (12 , 1) , (15 , 1.25) , (24 , 2)<br \/>\nFirst find the slope m of the line containing the two given points (12 ,1) and (24, 2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (2 \u2013 1) \/ (24 \u2013 12)<br \/>\nm = 1\/12<br \/>\nm = 0.08.<br \/>\nsubstitute the slope in the (12 ,1) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 1 = 0.08(x \u2013 12)<br \/>\ny \u20131 = 0.08x \u2013 0.96<br \/>\ny = 0.08x \u20130.96 + 1<br \/>\ny =0.08 x + 0.04<br \/>\nSo, y = 0.08x + 0.04 is a linear equation<\/p>\n<p><strong>WRITING FUNCTION RULES <\/strong>Write a function rule for the statement.<br \/>\nQuestion 9.<br \/>\nThe output is half of the input.<br \/>\nAnswer: y = \\(\\frac{x}{2}\\).<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is half of the input, will be ,<br \/>\ny = \\(\\frac{x}{2}\\).<\/p>\n<p>Question 10.<br \/>\nThe output is eleven more than the input.<br \/>\nAnswer: y = x + 11<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is eleven more than the input, will be ,<br \/>\ny = x + 11<\/p>\n<p>Question 11.<br \/>\nThe output is three less than the input.<br \/>\nAnswer: y = x &#8211; 3<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is three less than the input, will be ,<br \/>\ny = x &#8211; 3<\/p>\n<p>Question 12.<br \/>\nThe output is the cube of the input.<br \/>\nAnswer: y = x\u00b3<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is the cube of the input, will be ,<br \/>\ny = x\u00b3<\/p>\n<p>Question 13.<br \/>\nThe output is six times the input.<br \/>\nAnswer: y = 6x<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is six times the input, will be ,<br \/>\ny = 6x<\/p>\n<p>Question 14.<br \/>\nThe output is one more than twice the input.<br \/>\nAnswer: y = 2x + 1<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is one more than twice the input, will be ,<br \/>\ny = 2x + 1<\/p>\n<p><strong>EVALUATING A FUNCTION<\/strong> Find the value of y for the given value of x.<br \/>\nQuestion 15.<br \/>\ny = x + 5; x = 3<br \/>\nAnswer: y = 8<\/p>\n<p>Explanation:<br \/>\nGiven, y = x + 5<br \/>\nsubstitute x = 3 , we get<br \/>\ny = 3 + 5<br \/>\nSo, y = 8.<\/p>\n<p>Question 16.<br \/>\ny = 7x; x = &#8211; 5<br \/>\nAnswer:\u00a0 y = -35.<\/p>\n<p>Explanation:<br \/>\nGiven, y = 7x<br \/>\nsubstitute x = -5 , we get<br \/>\ny = 7(-5)<br \/>\nSo, y = -35.<\/p>\n<p>Question 17.<br \/>\ny = 1 &#8211; 2x; x = 9<br \/>\nAnswer: y = -17<\/p>\n<p>Explanation:<br \/>\nGiven, y = 1 &#8211; 2x<br \/>\nsubstitute x = 9 , we get<br \/>\ny = 1 &#8211; 2(9)<br \/>\ny = 1 &#8211; 18<br \/>\nSo, y = -17.<\/p>\n<p>Question 18.<br \/>\ny = 3x + 2; x = 0.5<br \/>\nAnswer: y = 5.5<\/p>\n<p>Explanation:<br \/>\nGiven, y = 3x + 2<br \/>\nsubstitute x = 0.5 , we get<br \/>\ny = 3(0.5) + 2<br \/>\ny = 3.5 + 2<br \/>\nSo, y = 5.5 .<\/p>\n<p>Question 19.<br \/>\ny = 2x<sup>3<\/sup>; x = 3<br \/>\nAnswer: y = 54<\/p>\n<p>Explanation:<br \/>\nGiven, y = 2x<sup>3<\/sup><br \/>\nsubstitute x = 3 , we get<br \/>\ny = 2(3)\u00b3<br \/>\ny = 2 \u00d7 27 = 54<br \/>\nSo, y = 54.<\/p>\n<p>Question 20.<br \/>\ny = \\(\\frac{x}{2}\\) + 9; x = &#8211; 12<br \/>\nAnswer: y = 3<\/p>\n<p>Explanation:<br \/>\nGiven, y = \\(\\frac{x}{2}\\) + 9<br \/>\nsubstitute x = -12 , we get<br \/>\ny = \\(\\frac{-12}{2}\\) + 9<br \/>\ny = -6 + 9<br \/>\nSo, y = 3 .<\/p>\n<p><strong>GRAPHING A FUNCTION<\/strong> Graph the function.<br \/>\nQuestion 21.<br \/>\ny = x + 4<br \/>\nAnswer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-49997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-24.png\" alt=\"\" width=\"474\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-24.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-24-300x261.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = x + 4 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 + 4 = 4 . co-ordinates are (0 , 4)<br \/>\nif x = 1 , then y = 1 + 4 = 5 . co-ordinates are (1 , 5)<br \/>\nif x = 2 , then y = 2 + 4 = 6 , co-ordinates are (2 , 6)<br \/>\nif x = 3 , then y = 3 + 4 = 7 , co-ordinates are (3 , 7)<br \/>\nThe co-ordinates (0 , 4) , (1 , 5) , (2 , 6) , (3 , 7) form a straight line .<\/p>\n<p>Question 22.<br \/>\ny = 2x<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25.png\" alt=\"\" width=\"499\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25-300x217.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = 2x\u00a0 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 2(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = 2(1) = 2 . co-ordinates are (1 , 2)<br \/>\nif x = 2 , then y = 2(2) = 4 , co-ordinates are (2 , 4)<br \/>\nif x = 3 , then y = 2(3) = 6 , co-ordinates are (3 , 6)<br \/>\nThe co-ordinates (0 , 0) , (1 , 2) , (2 , 4) , (3 , 6) form a straight line .<\/p>\n<p>Question 23.<br \/>\ny = &#8211; 5x + 3<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-49999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-26.png\" alt=\"\" width=\"497\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-26.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-26-300x220.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; 5x + 3 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =- 5(0) + 3 = 3 . co-ordinates are (0 , 3)<br \/>\nif x = 1 , then y = &#8211; 5(1) + 3 = -2 . co-ordinates are (1 , -2)<br \/>\nif x = 2 , then y = &#8211; 5(2) + 3 = -7 , co-ordinates are (2 , -7)<br \/>\nif x = 3 , then y = &#8211; 5(3) + 3 = -12 , co-ordinates are (3 , -12)<br \/>\nThe co-ordinates (0 , 3) , (1 , -2) , (2 , -7) , (3 , -12) form a straight line .<\/p>\n<p>Question 24.<br \/>\ny = \\(\\frac{x}{4}\\)<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-50000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-27.png\" alt=\"\" width=\"444\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-27.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-27-300x257.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = \\(\\frac{x}{4}\\) , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = \\(\\frac{0}{4}\\) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = \\(\\frac{1}{4}\\) = 0.25 . co-ordinates are (1 , 0.25)<br \/>\nif x = 2 , then y = \\(\\frac{2}{4}\\) = 0.5 , co-ordinates are (2 , 0.5)<br \/>\nif x = 3 , then y = \\(\\frac{3}{4}\\) = 0.75 , co-ordinates are (3 , 0.75)<br \/>\nThe co-ordinates (0 , 0) , (1 , 0.25) , (2 , 0.5) , (3 , 0.75) form a straight line .<\/p>\n<p>Question 25.<br \/>\ny = \\(\\frac{3}{2}\\)x + 1<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-50001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-28.png\" alt=\"\" width=\"439\" height=\"386\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-28.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-28-300x264.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = \\(\\frac{3}{2}\\)x + 1 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =\\(\\frac{3}{2}\\)(0) + 1 = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = \\(\\frac{3}{2}\\)(1) + 1= 2.5 . co-ordinates are (1 , 2.5)<br \/>\nif x = 2 , then y = \\(\\frac{3}{2}\\)(2) + 1 = 4 , co-ordinates are (2 , 4)<br \/>\nif x = 3 , then y = \\(\\frac{3}{2}\\)(3) + 1 = 5.5 , co-ordinates are (3 , 5.5)<br \/>\nThe co-ordinates (0 , 1) , (1 , 2.5) , (2 , 4) , (3 , 5.5) form a straight line .<\/p>\n<p>Question 26.<br \/>\ny = 1 + 0.5x<br \/>\nAnswer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-50002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-29.png\" alt=\"\" width=\"444\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-29.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-29-300x259.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = 1 + 0.5x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =1 + 0.5(0) = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = 1 + 0.5(1) = 1.5 . co-ordinates are (1 , 1.5)<br \/>\nif x = 2 , then y = 1 + 0.5(2) = 2 , co-ordinates are (2 , 2)<br \/>\nif x = 3 , then y = 1 + 0.5(3) = 2.5 , co-ordinates are (3 , 2.5)<br \/>\nThe co-ordinates (0 , 1) , (1 , 1.5) , (2 , 2) , (3 , 2.5)\u00a0 form a straight line .<\/p>\n<p><strong>MATCHING<\/strong> Match the graph with the function it represents.<br \/>\nA. y = \\(\\frac{x}{3}\\)<br \/>\nB. y = x + 1<br \/>\nC. y = &#8211; 2x + 6<br \/>\nQuestion 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 16\" width=\"150\" height=\"143\" \/><br \/>\nAnswer:\u00a0 B. y = x + 1.<\/p>\n<p>Explanation:<br \/>\nGiven , y = x + 1 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 + 1 = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = 1 + 1 = 2 . co-ordinates are (1 , 2)<br \/>\nif x = 2 , then y = 2 + 1 = 3 , co-ordinates are (2 , 3)<br \/>\nThe co-ordinates (0 , 1) , (1 , 2) , (2 , 3) form a straight line .<\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 17\" width=\"144\" height=\"143\" \/><br \/>\nAnswer: c. y = &#8211; 2x + 6<\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; 2x + 6 \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = &#8211; 2(0) + 6 = 6 . co-ordinates are (0 , 6)<br \/>\nif x = 1 , then y = &#8211; 2(1) + 6 = 4 . co-ordinates are (1 , 4)<br \/>\nif x = 2 , then y = &#8211; 2(2) + 6 = 2 , co-ordinates are (2 , 2)<br \/>\nif x = 3 , then y = &#8211; 2(3) + 6 = 0 , co-ordinates are (3 , 0)<br \/>\nThe co-ordinates (0 , 6) , (1 , 4) , (2 , 2) , (3 , 0) form a straight line .<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 18\" width=\"143\" height=\"152\" \/><br \/>\nAnswer: A. y = \\(\\frac{x}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven , y =\u00a0 \\(\\frac{x}{3}\\)\u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =\\(\\frac{0}{3}\\) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = \\(\\frac{1}{3}\\)= 0.3 . co-ordinates are (1 , 0.3)<br \/>\nif x = 2 , then y = \\(\\frac{2}{3}\\)= 0.6 , co-ordinates are (2 , 0.6)<br \/>\nThe co-ordinates (0 , 0) , (1 , 0.3) , (2 , 0.6) form a straight line .<\/p>\n<p>Question 30.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend graphs the function represented by the input-output table. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 19\" width=\"182\" height=\"192\" \/><br \/>\nAnswer: Yes , He is correct<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-73.png\" alt=\"\" width=\"307\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-73.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-73-300x78.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nOrdered pairs are (-1 , -4) , (1 , -2) , (3 ,0) , (5 , 2)<br \/>\nthese points form a straight line when graphed.<br \/>\nYes , He is correct<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA dolphin eats 30 pounds of fish per day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 20\" width=\"250\" height=\"147\" \/><br \/>\na. Write and graph a function that relates the number p of pounds of fish that a dolphin eats in d days.<br \/>\nb. How many total pounds of fish does a dolphin eat in 30 days?<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\na. Given , A dolphin eats 30 pounds of fish per day.<br \/>\nby each passing day eating fish is increased by the day passes .<br \/>\nSo, y = 30x is the function,<br \/>\nThe graph represents the function as<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25-1.png\" alt=\"\" width=\"499\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25-1.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-25-1-300x217.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nb. Given , A dolphin eats 30 pounds of fish per day.<br \/>\nthen for 30 days ,<br \/>\n30 \u00d7 30 = 900 pounds<br \/>\nSo, A dolphin eats 900 pounds of fish in 30 days<\/p>\n<p>Question 32.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou fill a fish tank with 55 gallons of water on Saturday. The water evaporates at a rate of 1.5 gallons per day. You plan to add water when the tank reaches 49 gallons. When will you add water? Justify your answer.<br \/>\nAnswer: As the action starts on Saturday , the tank will reach 49 gallons after 4 days , That is on Wednesday.<\/p>\n<p>Explanation:<br \/>\nGiven data ,, implies that slope of the function m = -1.5<br \/>\nThe y intercept b= 55,<br \/>\nThen the equation\u00a0 will be y = 55 &#8211; 1.5x<br \/>\nGiven , You plan to add water when the tank reaches 49 gallons.<br \/>\ndetermine x for y = 49 ,<br \/>\nSo, 49 = 55 &#8211; 1.5x ,<br \/>\n1.5x = 55 &#8211; 49<br \/>\n1.5x = 6<br \/>\nx = \\(\\frac{6}{1.5}\\)<br \/>\nx = 4.<\/p>\n<p>As the action starts on Saturday , the tank will reach 49 gallons after 4 days , That is on Wednesday.<\/p>\n<p><strong>USING AN EQUATION<\/strong> Find the value of x for the given value of y.<br \/>\nQuestion 33.<br \/>\ny = 5x &#8211; 7; y = &#8211; 22<br \/>\nAnswer: x = -3<\/p>\n<p>Explanation:<br \/>\nGiven, y = 5x &#8211; 7<br \/>\nx = \\(\\frac{y + 7}{5}\\)<br \/>\nsubstitute y = -22 , we get<br \/>\nx = \\(\\frac{-22 + 7}{5}\\)<br \/>\nx = \\(\\frac{- 15}{5}\\)<br \/>\nx = -3<br \/>\nSo, x = -3 .<\/p>\n<p>Question 34.<br \/>\ny = 9 &#8211; 7x; y = 37<br \/>\nAnswer: x = -4<\/p>\n<p>Explanation:<br \/>\nGiven, y = 9 &#8211; 7x<br \/>\nx = \\(\\frac{9 &#8211; y}{7}\\)<br \/>\nsubstitute y = 37 , we get<br \/>\nx = \\(\\frac{9 &#8211; 37}{7}\\)<br \/>\nx = \\(\\frac{- 28}{7}\\)<br \/>\nx = -4<br \/>\nSo, x = -4 .<\/p>\n<p>Question 35.<br \/>\ny = \\(\\frac{x}{4}\\) &#8211; 7; y = 2<br \/>\nAnswer: x = 36<\/p>\n<p>Explanation:<br \/>\nGiven, y = \\(\\frac{x}{4}\\) &#8211; 7<br \/>\nx = 4( y + 7)<br \/>\nsubstitute y = 2 , we get<br \/>\nx = 4( 2 + 7)<br \/>\nx = 4(9)<br \/>\nx = 36<br \/>\nSo, x = 36 .<\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou decide to make and sell bracelets. The cost of your materials is $84.00. You charge $3.50 for each bracelet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 21\" width=\"143\" height=\"153\" \/><br \/>\na. P Write a function that represents the profit for selling b bracelets.<br \/>\nb. Which variable is independent? dependent? Explain.<br \/>\nc. You will break even when the cost of your materials equals your income. How many bracelets must you sell to break even?<br \/>\nAnswer: a. A function that represents the profit for selling b bracelets is p = 3.5b &#8211; 84.<br \/>\nb. Here , the profit depends on the number of bracelets sold , b is the independent variable and p is the dependent variable.<br \/>\nc. To break even you must sell 24\u00a0 bracelets.<\/p>\n<p>Explanation:<br \/>\na. Given , The cost of your materials is $84.00. You charge $3.50 for each bracelet,<br \/>\nLet p be the profit , b be the number of bracelets sold,<br \/>\nSo, profit = income &#8211; cost .<br \/>\np = 3.5b &#8211; 84.<br \/>\nThus , A function that represents the profit for selling b bracelets is p = 3.5b &#8211; 84.<\/p>\n<p>b. Here , the profit depends on the number of bracelets sold , b is the independent variable and p is the dependent variable.<\/p>\n<p>c. set the income expression from part a equal to the cost of 84 and solve for b ,<br \/>\nSo, income = cost .<br \/>\n3.5b = 84 ,<br \/>\nb = \\(\\frac{84}{3.5}\\)<br \/>\nb = 24.<\/p>\n<p>To break even you must sell 24\u00a0 bracelets.<\/p>\n<p>Question 37.<br \/>\nMODELING REAL LIFE<br \/>\nA furniture store is having a sale where everything is 40% off.<br \/>\na. Write and graph a function that represents the amount of discount on an item at regular price.<br \/>\nb. You buy a bookshelf that has a regular price of $85. What is the sale price of the bookshelf?<br \/>\nAnswer: a. The function is y = 0.4x and the graph is given below.<br \/>\nb. The sale price of the bookshelf s $51.<\/p>\n<p>Explanation:<br \/>\na. A function that represents the amount of discount on an item at regular price is ,<br \/>\nGiven , 40% = 0.4 ,<br \/>\nTo find the percent of the number , we should multiply the number by the percent in the decimal form ,<br \/>\nso, the equation is d = 0.4p ,<br \/>\nlet us convert it in to a function form , y = 0.4x<br \/>\nwe know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0.4(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = 0.4(1)= 0.4 . co-ordinates are (1 , 0.4)<br \/>\nif x = 2 , then y =0.4(2) = 0.8 , co-ordinates are (2 , 0.8)<br \/>\nif x = 3 , then y = 0.4(3) = 1.2 , co-ordinates are (3 , 1.2)<br \/>\nThe co-ordinates (0 , 0) , (1 , 0.4) , (2 , 0.8) , (3 , 1.2) form a straight line .<br \/>\nThe graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-50466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-30.png\" alt=\"\" width=\"499\" height=\"358\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-30.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-30-300x215.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nb. Given , You buy a bookshelf that has a regular price of $85.<br \/>\nThe sale price of the bookshelf is ,<br \/>\nsubstituting the given price in p = 85 ,<br \/>\nit will be the discount d = 0.4 (85) = 34<br \/>\nThen the sale price is $85 &#8211; $34 = $51.<\/p>\n<p>So, The sale price of the bookshelf s $51.<\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou want to take a two-hour air boat tour. Which is a better deal, Snake Tours or Gator Tours? Use functions to justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-22.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 22\" width=\"560\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-22.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-22-300x117.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\nAnswer: By using functions , $50 &gt; $40 , So, Gator tours are cheaper than the snake tours .<\/p>\n<p>Explanation:<br \/>\nGiven , You want to take a two-hour air boat tour.<br \/>\nLet x be the hours of\u00a0 air boat tour and y be the cost of air boat tour ,<br \/>\nSnake tours , y = 25x<br \/>\nputt x = 2 ,<br \/>\nSo , y = 25 (2) = 50 .<br \/>\ny = 50.<\/p>\n<p>Gator tour , y = 35 + \\(\\frac{5}{2}\\)x<br \/>\nPut x = 2 ,<br \/>\nSo, y = 35 + \\(\\frac{5}{2}\\) x<br \/>\ny = 35 + 2.5x<br \/>\ny = 35 + 2.5 (2)<br \/>\ny = 35 + 5<br \/>\ny = 40 .<\/p>\n<p>Finally $50 &gt; $40 , So, Gator tours are cheaper than the snake tours<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graph of a function is a line that passes through the points (3, 2), (5, 8), and (8, y). What is the value of y?<br \/>\nAnswer: The value of y is 17 , so, The third given point is\u00a0<strong>(8, 17)<\/strong><\/p>\n<p>Explanation:<br \/>\nFirst find the slope m of the line containing the two given points (3,2) and (5,8)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (8 &#8211; 2) \/ (5 &#8211; 3)<br \/>\nm = 6 \/ 2<br \/>\nm = 3<strong><br \/>\n<\/strong>Then use the slope and one of the given points (3,2) to find the y-intercept<br \/>\ny = mx +<br \/>\n2 = 3(3) + b<br \/>\n2 = 9 + b<br \/>\n-7 = b<br \/>\nThe equation is\u00a0\u00a0\u00a0y = 3x -7<br \/>\nThen find the third point (8, y) by replacing x by 8<br \/>\ny = 3x -7<br \/>\ny = 3(8) -7<br \/>\ny = 24 -7<br \/>\ny = 17<\/p>\n<div>so the third given point is\u00a0<strong>(8, 17)<\/strong><\/div>\n<div><\/div>\n<p>Question 40.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nMake a table where the independent variable is the side length of a square and the dependent variable is the perimeter. Make a second table where the independent variable is the side length of a square and the dependent variable is the area. Graph both functions in the same coordinate plane. Compare the functions.<br \/>\nAnswer: The graph for the perimeter is linear , The graph for the Area is Quadratic .<\/p>\n<p>Explanation:<br \/>\nLet us say , s be the side length of the square ,<br \/>\nThen the perimeter is P = 4s ,<br \/>\nThe function will be y= 4x,<br \/>\nwe know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 4(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = 4(1) = 4 . co-ordinates are (1 , 4)<br \/>\nif x = 2 , then y = 4(2) =8 , co-ordinates are (2 , 8)<br \/>\nif x = 3 , then y = 4(3) = 0 , co-ordinates are (3 , 12)<br \/>\nThe co-ordinates (0 , 0) , (1 , 4) , (2 ,8) , (3 , 12) form a straight line .<\/p>\n<p>Table will be , <img loading=\"lazy\" class=\"alignnone size-full wp-image-50531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-31.png\" alt=\"\" width=\"304\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-31.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-31-300x92.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Let us say , s be the side length of the square ,<br \/>\nThen the Area is A = s\u00b2 ,<br \/>\nThe function will be y=x\u00b2,<br \/>\nwe know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0\u00b2 = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = 1\u00b2 = 1 . co-ordinates are (1 , 1)<br \/>\nif x = 2 , then y = 2\u00b2 =4 , co-ordinates are (2 , 4)<br \/>\nif x = 3 , then y = 3\u00b2 = 9 , co-ordinates are (3 , 9)<br \/>\nThe co-ordinates (0 , 0) , (1 , 1) , (2 ,4) , (3 , 9) form a straight line .<\/p>\n<p>Second table is <img loading=\"lazy\" class=\"alignnone size-full wp-image-50532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-32.png\" alt=\"\" width=\"304\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-32.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-32-300x93.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nThen the graph is\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-50535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-33.png\" alt=\"\" width=\"659\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-33.png 659w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-33-300x214.png 300w\" sizes=\"(max-width: 659px) 100vw, 659px\" \/><br \/>\nThe graph for the perimeter is linear , The graph for the Area is Quadratic .<\/p>\n<p>Question 41.<br \/>\n<strong>PUZZLE<\/strong><br \/>\nThe blocks that form the diagonals of each square are shaded. Each block has an area of one square unit. Find the \u201cgreen area\u201d of Square 20. Find the \u201cgreen area\u201d of Square 21. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-23.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions 7.2 23\" width=\"547\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-23.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-7.2-23-300x72.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><br \/>\nAnswer:\u00a0 The green area of the Square 20 is 46 square units and The green area of the Square 21 is 48 square units.<\/p>\n<p>Explanation:<br \/>\nGiven , Each block has an area of one square unit,<br \/>\nSquare 1 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 3 + 3 = 6 square units ,<br \/>\nSquare 2 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 4 + 4 = 8 square units ,<br \/>\nSquare 3 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 5 + 5 = 10 square units ,<br \/>\nSquare 4 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 6 + 6 = 12 square units,<br \/>\nSquare 5 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 7 + 7 = 14 square units ,<br \/>\nHere , The number of squares are increasing by one block with the square numbers.<br \/>\nSo for the , Square 20 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 23 + 23 = 46 square units,<br \/>\nAnd Square 21 has\u00a0 the diagonals of each square are shaded. the \u201cgreen area\u201d is 24 + 24 = 48 square units.<\/p>\n<h3><a id=\"Lesson _7.3 _Linear _Functions\"><\/a>Lesson 7.3 Linear Functions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing and Graphing Functions<br \/>\nWork with a partner. Each table shows a familiar pattern from geometry.<\/p>\n<ul>\n<li>Determine what the variables x and y represent. Then write a function rule that relates y to x.<\/li>\n<li>Is the function a linear function? Explain your reasoning.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 1\" width=\"666\" height=\"543\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-1.png 666w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-1-300x245.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><br \/>\nAnswer: All of them are explained below<\/p>\n<p>Explanation:<br \/>\nThe variables x and y represents a rectangle<br \/>\na. From the given table , Ordered pairs are (1 , 10) , (2 , 12) , (3 , 14) , (4 , 16)<br \/>\nFirst find the slope m of the line containing the two given points (1 ,-1) and (2, -2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (-2 \u2013 (-1)) \/ (2 \u2013 0)<br \/>\nm = -1 \/ 2 .<br \/>\nsubstitute the slope in the (1 , 10) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 10 = -1\/2 ( x \u20131)<br \/>\n2(y \u2013 10) = -x\u00a0 + 1<br \/>\n2y &#8211; 20 = -x+ 1<br \/>\n2y = -x\u00a0 + 21<br \/>\ny = \\(\\frac{-1}{2}\\) (x &#8211; 21)<br \/>\nSo ,\u00a0 y = \\(\\frac{-1}{2}\\) (x &#8211; 21) is linear function.<\/p>\n<p>b. The variables x and y represent a circle<br \/>\nOrdered pairs are (1 , 3.14 ) , (2 , 6.28) , (3 , 9.42) , (4 , 12.5 )<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (1 , 3.14 ) , (2 , 6.28)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6.28 \u20133.14) \/ (2\u2013 1)<br \/>\nm = 3.14\/1<br \/>\nm = 3.14<br \/>\nsubstitute the slope in the (8 , 4) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 3.14 =3.14 ( x \u20131)<br \/>\ny \u2013 3.14 = 3.14x \u2013 3.14<br \/>\ny = 3.14x \u2013 3.14 + 3.14<br \/>\ny = 3.14x<br \/>\nSo ,\u00a0 y = 3.14x\u00a0 is linear function.<br \/>\nWhere x is the diameter of the circle.<\/p>\n<p>c. The variables x and y represents a trapezoid<br \/>\na. From the given table , Ordered pairs are (1 , 5) , (2 , 6) , (3 , 7) , (4 , 8)<br \/>\nFirst find the slope m of the line containing the two given points (1 ,5) and (2, 6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6 \u2013 5) \/ (2 \u2013 1)<br \/>\nm = 1 .<br \/>\nsubstitute the slope in the (1 ,5) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny &#8211; 5 = 1(x &#8211; 1)<br \/>\ny &#8211; 5 = x &#8211; 1<br \/>\ny = x &#8211; 1 + 5<br \/>\ny = x + 4<br \/>\nSo, y = x + 4 is a linear equation<\/p>\n<p>d. The variables x and y represents a cube<br \/>\na. From the given table , Ordered pairs are (1 , 28) , (2 , 40) , (3 , 52) , (4 , 64)<br \/>\nFirst find the slope m of the line containing the two given points (1 ,28) and (2, 40)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (40 \u2013 28) \/ (2 \u2013 1)<br \/>\nm = 12 .<br \/>\nsubstitute the slope in the (1 ,28) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny &#8211; 28 = 12(x &#8211; 1)<br \/>\ny &#8211; 28 = 12x &#8211; 12<br \/>\ny = 12x &#8211; 12 + 28<br \/>\ny = 12x + 16<br \/>\nSo, y = 12x + 16 is a linear equation.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 2\" width=\"188\" height=\"67\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the graph to write a linear function that relates y to x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 3\" width=\"156\" height=\"140\" \/><br \/>\nAnswer: the linear function is y = \\(\\frac{-1}{2}\\)x -1.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-4 , 1) , (-2 , 0 ) , (0 , -1) , ( 2, -2 )<br \/>\nFirst find the slope m of the line containing the two given points (0 ,-1) and (2, -2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (-2 \u2013 (-1)) \/ (2 \u2013 0)<br \/>\nm = -1 \/ 2 .<br \/>\nBecause the line crosses the y axis at ( 0, -1 ) , The y intercept is -1.<br \/>\nSo , the linear function is y = \\(\\frac{-1}{2}\\)x -1.<\/p>\n<p>Question 2.<br \/>\nUse the table to write a linear function that relates y to x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 4\" width=\"194\" height=\"69\" \/><br \/>\nAnswer: the linear function is y = (0)x + 2.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (-2 , 2) , (-1 , 2) , (0 , 2) , (1 , 2)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (0 ,2) and (1, 2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (2 \u2013 2) \/ (1 \u2013 0)<br \/>\nm = 0<br \/>\nBecause the line crosses the y axis at ( 0, 2 ) , The y intercept is 2.<br \/>\nSo , the linear function is y = (0)x + 2.<\/p>\n<p>Question 3.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe rate of descent doubles. Repeat parts (a) and (b).<br \/>\nAnswer: a. the linear function is y = -1x + 65.<br \/>\nb. The slope indicates that the height decreases 1000 feet per minute.<br \/>\nThe y intercept indicates that the descent begins at a cruising altitude of 65,000 feet.<\/p>\n<p>Explanation:<br \/>\na. From the Given table , The rate of descents is 5<br \/>\nIf it doubles , then The rate of descents is 10.<br \/>\nThe the ordered pairs will be (0 , 65) , (10 ,55) , (20 , 45) .<br \/>\nFirst find the slope m of the line containing the two given points (0 ,65) and (10, 55)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (55 \u2013 65) \/ (10 \u2013 0)<br \/>\nm = -10 \/ 10<br \/>\nm = -1<br \/>\nBecause the line crosses the y axis at ( 0, 65 ) , The y intercept is 65.<br \/>\nSo , the linear function is y = -1x + 65.<\/p>\n<p>b. The slope indicates that the height decreases 1000 feet per minute.<br \/>\nThe y intercept indicates that the descent begins at a cruising altitude of 65,000 feet.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 4.<br \/>\n<strong>WRITING A LINEAR FUNCTION<\/strong><br \/>\nUse the graph to write a linear function that relates y to x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 5\" width=\"148\" height=\"151\" \/><br \/>\nAnswer:\u00a0 The linear function is y = -4x -2 .<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-2 , 6) , (-1 , 2 ) , (0 , -2) , ( 1, -6 )<br \/>\nFirst find the slope m of the line containing the two given points (0 ,-2) and (1, -6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (-6 \u2013 (-2)) \/ (1 \u2013 0)<br \/>\nm = -4 .<br \/>\nBecause the line crosses the y axis at ( 0, -2) , The y intercept is -2.<br \/>\nSo , the linear function is y = -4x -2 .<\/p>\n<p>Question 5.<br \/>\n<strong>INTERPRETING A LINEAR FUNCTION<\/strong><br \/>\nThe table shows the revenue R (in millions of dollars) of a company when it spends A (in millions of dollars) on advertising.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 6\" width=\"381\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-6.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-6-300x50.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\na. Write and graph a linear function that relates R to A.<br \/>\nb. Interpret the slope and the y-intercept.<br \/>\nAnswer:\u00a0 a. The linear function is y = 2x + 2. and the graph is shown below<br \/>\nb. The slope indicates that the increasing in the amount of spending on advertising by 2 million dollars<br \/>\nThe y intercept indicates that the Revenue begins to increasing from the 2 million dollars.<\/p>\n<p>Explanation:<br \/>\na. From the given table ,<br \/>\nThe the ordered pairs will be (0 , 2) , (2 ,6) , (4 , 10) , (6 , 14) , (8 ,18) .<br \/>\nThe graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-34.png\" alt=\"\" width=\"439\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-34.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-34-300x258.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\nFirst find the slope m of the line containing the two given points (0 ,2) and (2, 6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6 \u2013 2) \/ (2 \u2013 0)<br \/>\nm = 4 \/ 2<br \/>\nm = 2<br \/>\nBecause the line crosses the y axis at ( 0, 2 ) , The y intercept is 2.<br \/>\nSo , the linear function is y = 2x + 2.<\/p>\n<p>b. The slope indicates that the increasing in the amount of spending on advertising by 2 million dollars<br \/>\nThe y intercept indicates that the Revenue begins to increasing from the 2 million dollars.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\nManager A earns $15 per hour and receives a $50 bonus. The graph shows the earnings of Manager B. (a) Which manager has a greater hourly wage? (b) After how many hours does Manager B earn more money than Manager A?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 7\" width=\"197\" height=\"178\" \/><br \/>\nAnswer: a. Manager B has the greater hourly wage than Manager A .<br \/>\nb. As manager A receives a $50 bonus , Manager B has to work an hour extra to earn more money than Manager A .<\/p>\n<p>Explanation:<br \/>\na. Manager A earns $15 per hour and receives a $50 bonus.<br \/>\nThe ordered pairs will be \u00a0(0 , 0) , (1 , 15) , (2 , 30) , (3 , 45)<br \/>\nThe graph shows the earnings of Manager B.<br \/>\nOrdered pairs from the graph are \u00a0(0 , 0) , (1 , 25) , (2 , 50) , (3 , 75)<br \/>\nSo, Manager B has the greater hourly wage than Manager A .<\/p>\n<p>b. As manager A receives a $50 bonus , Manager B has to work an hour extra to earn more money than Manager A .<\/p>\n<p>Question 7.<br \/>\nEach month, you start with 2 gigabytes of data and use 0.08 gigabyte per day. The table shows the amount (in gigabytes) of data that your friend has left days after the start of each month. Who runs out of data first? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 8\" width=\"175\" height=\"137\" \/><br \/>\nAnswer:\u00a0 you will be run out of data first<\/p>\n<p>Explanation:<br \/>\na. Given , Each month, you start with 2 gigabytes of data and use 0.08 gigabyte per day.<br \/>\nLet x be the number of days and y be the total data in gigabytes.<br \/>\nSo, y = -0.08x + 2 ,<br \/>\nYou will be out of data if , -0.08x + 2 = 0 ,<br \/>\n-0.08x + 2 = 0<br \/>\n2 = 0.08x<br \/>\nx = \\(\\frac{2}{0.08}\\)<br \/>\nx = 25.<br \/>\nHence ,you will be run out of data in 25 days.<br \/>\nb. Daily data usage for the friend will be given by the slope of the graph.<br \/>\nThe the ordered pairs will be (0 , 3) , (7 ,2.3) , (14 , 1.6) .<br \/>\nFirst find the slope m of the line containing the two given points (7 ,2.3) and (14, 1.6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (1.6 \u2013 2.3) \/ (14 \u2013 7)<br \/>\nm = -0.7 \/ 7<br \/>\nm = -0.1<br \/>\nBecause the line crosses the y axis at ( 0, 3 ) , The y intercept is 3.<br \/>\nSo , the linear function is y = -0.1x + 3.<br \/>\nYour friend will be out of data if ,<br \/>\n-0.1x + 3 = 0<br \/>\n3 = 0.1x<br \/>\nx = \\(\\frac{3}{0.1}\\)<br \/>\nx = 30 .<br \/>\nHence ,Friend will be run out of data in 30 days<\/p>\n<p>So , you will be run out of data first<\/p>\n<h3><a id=\"Linear _Functions _Homework _&amp; _Practice _7.3\"><\/a>Linear Functions Homework &amp; Practice 7.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write a function rule for the statement. Then graph the function.<\/strong><br \/>\nQuestion 1.<br \/>\nThe output is ten less than the input.<br \/>\nAnswer: y = x &#8211; 10.<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is ten less than the input, will be ,<br \/>\ny = x &#8211; 10.<\/p>\n<p>Question 2.<br \/>\nThe output is one-third of the input.<br \/>\nAnswer: y = \\(\\frac{x}{3}\\)<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is one-third of the input, will be ,<br \/>\ny = \\(\\frac{x}{3}\\) .<\/p>\n<p>Solve the system.<br \/>\nQuestion 3.<br \/>\ny = x + 5<br \/>\ny = &#8211; 3x + 1<br \/>\nAnswer: X = 0 , Y = 5<\/p>\n<p class=\"answerHeader\">Explanation:<br \/>\n<span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-39\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-40\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-41\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212<\/span><\/span><span id=\"MJXc-Node-42\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">3<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-45\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\"> &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-(1)<br \/>\n<\/span><span id=\"MathJax-Element-6-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-50\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-51\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-52\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-53\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-54\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\"> &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;(2)<br \/>\n<\/span><span style=\"font-size: 16px;\">Substitute\u00a0<\/span><span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-59\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-62\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-63\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\"> in equation (1)<br \/>\n<\/span><span id=\"MJXc-Node-68\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-69\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-70\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><span id=\"MJXc-Node-71\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-72\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212<\/span><\/span><span id=\"MJXc-Node-73\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">3<\/span><\/span><span id=\"MJXc-Node-74\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-75\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-76\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<br \/>\n<\/span><\/span><span style=\"font-size: 16px;\">Solve it for X<br \/>\n<\/span><span id=\"MJXc-Node-81\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-82\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-83\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">3<\/span><\/span><span id=\"MJXc-Node-84\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-85\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-86\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><span id=\"MJXc-Node-87\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">\u2212<\/span><\/span><span id=\"MJXc-Node-88\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<br \/>\n<\/span><\/span><span id=\"MJXc-Node-93\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">4<\/span><\/span><span id=\"MJXc-Node-94\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-95\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-96\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">0<br \/>\n<\/span><\/span><span id=\"MJXc-Node-101\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-102\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-103\" class=\"mjx-mfrac\" style=\"font-size: 16px;\"><span class=\"mjx-box MJXc-stacked\"><span class=\"mjx-numerator\"><span id=\"MJXc-Node-104\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">0\/<\/span><\/span><\/span><span class=\"mjx-denominator\"><span id=\"MJXc-Node-105\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">4<\/span><\/span><\/span><\/span><\/span><span id=\"MJXc-Node-106\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-107\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">0<br \/>\nX = 0<br \/>\n<\/span><\/span><span style=\"font-size: 16px;\">Substitute\u00a0<\/span><span id=\"MathJax-Element-12-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-108\" class=\"mjx-math\"><span id=\"MJXc-Node-109\" class=\"mjx-mrow\"><span id=\"MJXc-Node-110\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-113\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-114\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\"> in equation (1)<br \/>\n<\/span><span id=\"MJXc-Node-119\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-120\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-121\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">0<\/span><\/span><span id=\"MJXc-Node-122\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">+<\/span><\/span><span id=\"MJXc-Node-123\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<br \/>\n<\/span><\/span><span id=\"MJXc-Node-128\" class=\"mjx-mi\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-129\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-130\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">5<\/span><\/span><\/p>\n<p>Question 4.<br \/>\nx + y = &#8211; 4<br \/>\n6x + 2y = 4<br \/>\nAnswer:\u00a0 X = 3 , <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\"><span id=\"MJXc-Node-128\" class=\"mjx-mi\" style=\"font-size: 16px;\">Y<\/span><span id=\"MJXc-Node-129\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">= -7 .<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Explanation:<br \/>\n<span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-39\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">2Y<\/span><\/span><span id=\"MJXc-Node-40\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=<\/span><\/span><span id=\"MJXc-Node-41\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22126<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-(1)<br \/>\n<\/span><span id=\"MathJax-Element-6-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-46\" class=\"mjx-math\"><span id=\"MJXc-Node-47\" class=\"mjx-mrow\"><span id=\"MJXc-Node-48\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-49\" class=\"mjx-mrow\"><span id=\"MJXc-Node-50\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-51\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= &#8211;<\/span><\/span><span id=\"MJXc-Node-52\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X-4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;(2)<br \/>\n<\/span><span style=\"font-size: 16px;\">Substitute\u00a0<\/span><span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-59\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= &#8211;<\/span><\/span><span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X-4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0in equation (1)<br \/>\n<\/span><span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-39\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">2Y <\/span><\/span><span id=\"MJXc-Node-40\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <\/span><\/span><span id=\"MJXc-Node-41\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22126<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n2 ( <span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">&#8211;<\/span><\/span><span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X &#8211; 4 ) = <span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-41\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">\u22126<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\">X <\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+ 4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n-2X &#8211; 8 = -6X + 4<br \/>\n6X -2X = 8 + 4<br \/>\n4X = 12<br \/>\nX = 3<br \/>\n<span style=\"font-size: 16px;\">Substitute\u00a0<\/span><span id=\"MathJax-Element-12-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-108\" class=\"mjx-math\"><span id=\"MJXc-Node-109\" class=\"mjx-mrow\"><span id=\"MJXc-Node-110\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mi\">X<\/span><span id=\"MJXc-Node-113\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">=3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0in equation (2)<br \/>\n<\/span><span id=\"MJXc-Node-119\" class=\"mjx-mi\" style=\"font-size: 16px;\">Y<\/span><span id=\"MJXc-Node-120\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">=<span id=\"MJXc-Node-60\" class=\"mjx-mo\">&#8211; 3 <\/span>&#8211; 4<\/span><\/span><span id=\"MJXc-Node-123\" class=\"mjx-mn\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\"><br \/>\n<\/span><\/span><span id=\"MJXc-Node-128\" class=\"mjx-mi\" style=\"font-size: 16px;\">Y<\/span><span id=\"MJXc-Node-129\" class=\"mjx-mo\" style=\"font-size: 16px;\"><span class=\"mjx-char MJXc-TeX-main-R\">= -7 .<\/span><\/span><br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Question 5.<br \/>\n&#8211; 4x + 3y = 14<br \/>\ny = 2x + 8<br \/>\nAnswer:\u00a0 X = -5 , <span style=\"font-size: 16px;\"><span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\"><span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\"><span id=\"MJXc-Node-129\" class=\"mjx-mo\" style=\"font-size: 16px;\">Y = -2 .<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Explanation:<br \/>\n<span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-39\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">3Y <\/span><\/span><span id=\"MJXc-Node-40\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= 4<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+14<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-(1)<br \/>\n<\/span><span style=\"font-size: 16px;\">Y = 2X + 8 &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;(2)<br \/>\n<\/span><span style=\"font-size: 16px;\">Substitute\u00a0<\/span><span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-59\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Y<\/span><\/span><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= <span style=\"font-size: 16px;\">2X + 8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"font-size: 16px;\">\u00a0in equation (1)<br \/>\n<span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-39\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">3Y <\/span><\/span><span id=\"MJXc-Node-40\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">= 4<\/span><\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">+14<\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n3(<span id=\"MathJax-Element-7-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-55\" class=\"mjx-math\"><span id=\"MJXc-Node-56\" class=\"mjx-mrow\"><span id=\"MJXc-Node-57\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-58\" class=\"mjx-mrow\"><span id=\"MJXc-Node-60\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\">2X + 8) = <span id=\"MathJax-Element-5-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-35\" class=\"mjx-math\"><span id=\"MJXc-Node-36\" class=\"mjx-mrow\"><span id=\"MJXc-Node-37\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-38\" class=\"mjx-mrow\"><span id=\"MJXc-Node-40\" class=\"mjx-mo\">4<\/span><span id=\"MJXc-Node-43\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">X<\/span><\/span><span id=\"MJXc-Node-44\" class=\"mjx-mo\">+14<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n6X + 24 = 4X + 14<br \/>\n6X &#8211; 4X = 14 &#8211; 24<br \/>\n2X = -10<br \/>\nX = -5<br \/>\n<span id=\"MJXc-Node-61\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">Substitute\u00a0<span id=\"MathJax-Element-12-Frame\" class=\"mjx-chtml MathJax_CHTML\" style=\"font-size: 16px;\"><span id=\"MJXc-Node-108\" class=\"mjx-math\"><span id=\"MJXc-Node-109\" class=\"mjx-mrow\"><span id=\"MJXc-Node-110\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-111\" class=\"mjx-mrow\"><span id=\"MJXc-Node-112\" class=\"mjx-mi\">X<\/span><span id=\"MJXc-Node-113\" class=\"mjx-mo\">= -5<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0in equation (2)<br \/>\n<span id=\"MJXc-Node-119\" class=\"mjx-mi\" style=\"font-size: 16px;\">Y<\/span><span id=\"MJXc-Node-120\" class=\"mjx-mo\" style=\"font-size: 16px;\">= 2(-5) + 8<\/span><span id=\"MJXc-Node-123\" class=\"mjx-mn\" style=\"font-size: 16px;\"><br \/>\n<\/span><span id=\"MJXc-Node-128\" class=\"mjx-mi\" style=\"font-size: 16px;\">Y<\/span><span id=\"MJXc-Node-129\" class=\"mjx-mo\" style=\"font-size: 16px;\">= -10 + 8<br \/>\nY = -2.<\/span><\/span><\/span><br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>WRITING AND GRAPHING FUNCTIONS<\/strong> The table shows a familiar pattern from geometry. (a) Determine what the variables x and y represent. Then write a function rule that relates y to x. (b) Is the function a linear function? Explain your reasoning. (See Exploration 1, p. 289.)<br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 9\" width=\"241\" height=\"178\" \/><br \/>\nAnswer: a. The variables x and y represent a right angle triangle<br \/>\nb. y = 2x\u00a0 is linear function.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs<br \/>\nOrdered pairs are\u00a0 (1 , 2) , (2 , 4) ,\u00a0 (3 , 6 ) , (4 , 8), (5 , 10 ) .<br \/>\na. the variables x and y represent a right angle triangle<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (1 , 2) , (2 , 4)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (4 \u2013 2) \/ (2\u2013 1)<br \/>\nm = 2\/1<br \/>\nm = 2<br \/>\nb. substitute the slope in the (2 , 4) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 4 = 2 ( x \u2013 2)<br \/>\ny \u2013 4 = 2x \u2013 4<br \/>\ny = 2x \u2013 4 + 4<br \/>\ny = 2x<br \/>\nSo ,\u00a0 y = 2x\u00a0 is linear function.<\/p>\n<p>Given side of triangle is 4 then x= 4\/2 = 2<br \/>\nx = 2 and y = 4.<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 10\" width=\"239\" height=\"174\" \/><br \/>\nAnswer: y = 3.14x\u00a0 is linear function. and The variables x and y represent a circle<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (1 , 3.14 ) , (2 , 6.28) , (3 , 9.42) , (4 , 12.5 )<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (1 , 3.14 ) , (2 , 6.28)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6.28 \u20133.14) \/ (2\u2013 1)<br \/>\nm = 3.14\/1<br \/>\nm = 3.14<br \/>\nsubstitute the slope in the (8 , 4) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 3.14 =3.14 ( x \u20131)<br \/>\ny \u2013 3.14 = 3.14x \u2013 3.14<br \/>\ny = 3.14x \u2013 3.14 + 3.14<br \/>\ny = 3.14x<br \/>\nSo ,\u00a0 y = 3.14x\u00a0 is linear function.<br \/>\nWhere x is the diameter of the circle.<\/p>\n<p><strong>WRITING LINEAR FUNCTIONS<\/strong> Use the graph or table to write a linear function that relates y to x.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 11\" width=\"143\" height=\"133\" \/><br \/>\nAnswer: The linear function is y = \\(\\frac{4}{3}\\)x +2<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-3 , -2) , (0 , 2 ) , (3 , 6) , ( 6, 10 )<br \/>\nFirst find the slope m of the line containing the two given points (3 ,6) and (6, 10)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (10 \u2013 6) \/ (6 \u2013 3)<br \/>\nm = 4\/3 .<br \/>\nBecause the line crosses the y axis at ( 0, 2) , The y intercept is 2.<br \/>\nSo , the linear function is y = \\(\\frac{4}{3}\\)x +2 .<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 12\" width=\"146\" height=\"138\" \/><br \/>\nAnswer: The linear function is y = (0)x +3 .<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-2 , 3) , (-1 , 3 ) , (0 , 3) , ( 1, 3 ) , (2 , 3)<br \/>\nFirst find the slope m of the line containing the two given points (1 ,3) and (2, 3)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (3 \u2013 3) \/ (2 \u2013 1)<br \/>\nm = 0 .<br \/>\nBecause the line crosses the y axis at ( 0, 3) , The y intercept is 3.<br \/>\nSo , the linear function is y = (0)x +3 .<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 13\" width=\"187\" height=\"68\" \/><br \/>\nAnswer: The linear function is y = \\(\\frac{-1}{4}\\)x + 0.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (-8 , 2) , (-4 , 1) , (0 , 0) , (4 , -1)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (-8 ,2) and (-4, 1)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (1 \u2013 2) \/ (-4 \u2013 (-8))<br \/>\nm = -1\/4<br \/>\nBecause the line crosses the y axis at ( 0, 0 ) , The y intercept is 0.<br \/>\nSo , the linear function is y = \\(\\frac{-1}{4}\\)x + 0.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 14\" width=\"177\" height=\"71\" \/><br \/>\nAnswer: The linear function is y = \\(\\frac{2}{3}\\)x + 5.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (-3 , 3) , (0 , 5) , (3 , 7) , (6 , 9)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (3 ,7) and (6, 9)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (9 \u2013 7) \/ (6 \u2013 3)<br \/>\nm = 2\/3<br \/>\nBecause the line crosses the y axis at ( 0, 5 ) , The y intercept is 5.<br \/>\nSo , the linear function is y = \\(\\frac{2}{3}\\)x + 5.<\/p>\n<p>Question 12.<br \/>\n<strong>INTERPRETING A LINEAR FUNCTION<\/strong><br \/>\nThe table shows the length y (in inches) of a person\u2019s hair after x months.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 15\" width=\"160\" height=\"109\" \/><br \/>\na. Write and graph a linear function that relates y to x.<br \/>\nb. Interpret the slope and the y-intercept.<br \/>\nAnswer: a. The linear function is y = 0.5x + 11.<br \/>\nb. The slope indicates that the increasing in the hair length<br \/>\nThe y intercept indicates that the increasing in hair length by time.<\/p>\n<p>Explanation:<br \/>\na. Given ,<br \/>\nThe ordered pairs will be (0 , 11) , (3 ,12.5) , (6 , 14) .<br \/>\nThe graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-35.png\" alt=\"\" width=\"469\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-35.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-35-300x258.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><br \/>\nFirst find the slope m of the line containing the two given points (3 ,12.5) and (6 , 14)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (14 \u2013 12.5) \/ (6 \u2013 3)<br \/>\nm = 1.5 \/ 3<br \/>\nm = 0.5<br \/>\nBecause the line crosses the y axis at ( 0, 11 ) , The y intercept is 11.<br \/>\nSo , the linear function is y = 0.5x + 11.<\/p>\n<p>b. The slope indicates that the increasing in the hair length<br \/>\nThe y intercept indicates that the increasing in hair length by time.<\/p>\n<p>Question 13.<br \/>\n<strong>INTERPRETING A LINEAR FUNCTION<\/strong><br \/>\nThe table shows the percent (in decimal form) of battery power remaining x hours after you turn on a laptop computer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 16\" width=\"326\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-16.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-16-300x62.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\na. Write and graph a linear function that relates y to x.<br \/>\nb. Interpret the slope, the x-intercept, and the y-intercept.<br \/>\nc. After how many hours is the battery power at75%?<br \/>\nAnswer: a. The linear function is y = -0.2x + 1.<br \/>\nb. given below the explanation.<br \/>\nc. Battery will be 75% after 1.25 hours.<\/p>\n<p>Explanation:<br \/>\na. Given ,<br \/>\nThe ordered pairs will be (0 , 1) , (2 ,0.6) , (4 , 0.2) .<br \/>\nThe graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-36.png\" alt=\"\" width=\"435\" height=\"373\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-36.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-36-300x257.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\nFirst find the slope m of the line containing the two given points (2 ,0.6) and (4 , 0.2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (0.2 \u2013 0.6) \/ (4 \u2013 2)<br \/>\nm = -0.4 \/ 2<br \/>\nm = -0.2<br \/>\nBecause the line crosses the y axis at ( 0, 1 ) , The y intercept is 1.<br \/>\nSo , the linear function is y = -0.2x + 1.<\/p>\n<p>b. Slope is -0.2 which means that as time increases by 1 hour, Battery power remaining decreases by 20% .<br \/>\ny intercept is 1, which means initially the battery power remaining before usage was 100%.<br \/>\nx intercept is 5 which means the battery remaining will be 0 after 5 hours.<\/p>\n<p>c. battery percent will be 75% of 0.75 if ,<br \/>\n-0.2x + 1 = 0.75<br \/>\n0.2x = 1 &#8211; 0.75<br \/>\nx = 0.25\/0.2<br \/>\nx = 1.25<br \/>\nBattery will be 75% after 1.25 hours.<\/p>\n<p>Question 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe number y of calories burned after x minutes of kayaking is represented by the linear function y = 4.5x. The graph shows the number of calories burned by hiking.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-17.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 17\" width=\"175\" height=\"195\" \/><br \/>\na. Which activity burns more calories per minute?<br \/>\nb. You perform each activity for 45 minutes. How many total calories do you burn? Justify your answer.<br \/>\nAnswer: a. hiking burns more calories than kayaking .<br \/>\nb. In kayaking, 202.5 calories are burnt per minute. and In hiking , 225 calories are burnt per minute.<\/p>\n<p>Explanation:<br \/>\na. The number y of calories burned after x minutes of kayaking is represented by the linear function y = 4.5x.<br \/>\nSo, The ordered pairs of the graph are (0 , 0) , (1 , 4.5) , (2 , 9) , (3, 13.5)<br \/>\nHere , In kayaking burns 4.5 calories per minute .<br \/>\nFor hiking ,<br \/>\nThe ordered pairs of the graph are (0 , 0) , (1 , 5) , (2 , 10) , (3, 15)<br \/>\nHere , In hiking burns 5 calories per minute.<br \/>\nThus , hiking burns more calories than kayaking .<\/p>\n<p>b. Given , perform each activity for 45 minutes.<br \/>\nLiner function of the kayaking is y = 4.5x<br \/>\nsubstitute x = 45 in equation<br \/>\ny = 4.5 (45)<br \/>\ny = 202.5<br \/>\nIn kayaking, 202.5 calories are burnt per minute.<br \/>\nLinear function of the hiking is y = 5x<br \/>\nsubstitute x = 45 in equation<br \/>\ny = 5 (45)<br \/>\ny = 225<br \/>\nIn hiking , 225 calories are burnt per minute.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and a friend race each other. You give your friend a 50-foot head start. The distance y (in feet) your friend runs after x seconds is represented by the linear function y = 14x + 50. The table shows your distance at various times throughout the race. For what distances will you win the race? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-18.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 18\" width=\"360\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-18.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-18-300x56.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\nAnswer: you will win the race for distances greater than 190 feet<\/p>\n<p>Explanation:<br \/>\nThe distance y (in feet) your friend runs after x seconds is represented by the linear function y = 14x + 50.<br \/>\nThe slope of the line is 14 so , your friend runs at the rate of 14 ft per second<br \/>\nTo find your rate , the ordered pairs are (2 , 38) , (4 , 76) , (6 , 114) , (8 , 152)<br \/>\nFirst find the slope m of the line containing the two given points (2 ,38) and (4 , 76)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (76 \u2013 38) \/ (4 \u2013 2)<br \/>\nm = 38 \/ 2<br \/>\nm = 19<br \/>\nYou are running at the rate of 19 ft per second.<br \/>\nTo get the linear equation , substitute the slope in the (2 , 38) to get point slope to form a line.<br \/>\nThen we have , y = 19x<br \/>\nNow if x = 10 , to run faster then ,<br \/>\ny = 19(10)<br \/>\ny = 190 .<br \/>\nYour friend linear equation is y = 14x + 50 .<br \/>\nif x = 10 ,then<br \/>\ny = 14(10) + 50<br \/>\ny = 140 + 50<br \/>\ny = 190.<br \/>\nSo , for x &gt; 10 , means you will run farther than your friend which means you would win the race .<br \/>\nTherefore, you will win the race for distances greater than 190 feet.<\/p>\n<p>Question 16.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou and your friend are saving money to buy bicycles that cost $175 each. You have $45 to start and save an additional $5 each week. The graph shows the amount y(in dollars) that your friend has after x weeks. Who can buy a bicycle first? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-19.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 19\" width=\"181\" height=\"194\" \/><br \/>\nAnswer: \u00a0your friend will but the bicycle first.<\/p>\n<p>Explanation:<br \/>\nGiven , your friend savings are<br \/>\nthe ordered pairs are (0,15) and (3,39)<br \/>\nFirst find the slope m of the line containing the two given points (0,15) and (3,39)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (39 \u2013 15) \/ (3 \u2013 0)<br \/>\nm = 24 \/ 3<br \/>\nm = 8<br \/>\nBecause the line crosses the y axis at ( 0, 15 ) , The y intercept is 15.<br \/>\nSo , the linear function is y = 8x + 15.<br \/>\nto buy bicycles that cost $175 each<br \/>\nif y = 175 , then<br \/>\n175 = 8x + 15<br \/>\n8x = 175 &#8211; 15<br \/>\nx = 160\/8<br \/>\nx = 20<br \/>\nSo, your friend need 20 weeks to buy the bicycle<br \/>\nGiven, You have $45 to start and save an additional $5 each week<br \/>\nSo , the linear function will be y = 5x + 45.<br \/>\nto buy bicycles that cost $175 each<br \/>\nif y = 175 , then<br \/>\n175 = 5x + 45<br \/>\n5x = 175 &#8211; 45<br \/>\nx = 130\/5<br \/>\nx = 26<br \/>\nSo, you need 26 weeks to buy the bicycle.<br \/>\nHence, your friend will but the bicycle first.<\/p>\n<p>Question 17.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs every linear equation a linear function? Explain your reasoning.<br \/>\nAnswer: All\u00a0linear equations\u00a0produce straight lines when graphed, not all\u00a0linear equations\u00a0produce\u00a0linear functions. In order to be a\u00a0linear function, a graph must be both\u00a0linear\u00a0(a straight line) and a\u00a0function\u00a0(matching\u00a0each\u00a0x-value to only one y-value).<\/p>\n<p>Question 18.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe heat index is calculated using the relative humidity and the temperature. For every 1 degree increase in the temperature from 94\u00b0F to 97\u00b0F at 75% relative humidity, the heat index rises 4\u00b0F. On a summer day, the relative humidity is 75%, the temperature is 94\u00b0F, and the heat index is 124\u00b0F. Estimate the heat index when the relative humidity is 75% and the temperature is 100\u00b0F. Use a function to justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-20.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions 7.3 20\" width=\"182\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-20.png 182w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-7.3-20-150x150.png 150w\" sizes=\"(max-width: 182px) 100vw, 182px\" \/><br \/>\nAnswer:\u00a0 Heat index is 148\u00b0F<\/p>\n<p>Explanation:<br \/>\nThe form of linear equation is y = mx + c<br \/>\nand the slope of the function is given by m = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nLet y be the heat index and x be the temperature<br \/>\nGiven , (94, 124)<br \/>\nFor every 1 degree increase in the temperature from 94\u00b0F to 97\u00b0F at 75% relative humidity, the heat index rises 4\u00b0F<br \/>\nthat is m = 4<br \/>\nSince the line passes through (94, 124) means<br \/>\n124 = 4x + c<br \/>\n124 = 4(94) + c<br \/>\n124 = 376 + c<br \/>\nc = 124 &#8211; 376<br \/>\nc = -252<br \/>\nLinear function for the heat index is y = 4x &#8211; 252<br \/>\nput x = 100<br \/>\nSo, y = 4(100) &#8211; 252<br \/>\ny = 400 &#8211; 252<br \/>\ny = 148.<br \/>\nFinally, Heat index is 148\u00b0F.<\/p>\n<h3><a id=\"Lesson _7.4 _Comparing _Linear _and _Non _Linear _Functions\"><\/a><br \/>\nLesson 7.4 Comparing Linear and Non Linear Functions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Comparing Functions<br \/>\nWork with a partner. Each equation represents the height h (in feet) of a falling object after t seconds.<\/p>\n<ul>\n<li>Graph each equation. Explain your method.<\/li>\n<li>Decide whether each graph represents a or function.<\/li>\n<li>Compare the falling objects.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 1\" width=\"643\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-1.png 643w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-1-300x240.png 300w\" sizes=\"(max-width: 643px) 100vw, 643px\" \/><br \/>\nAnswer: Explained below<\/p>\n<p>Explanation:<br \/>\na. Given, h = 300 &#8211; 15t can be written as y = 300 &#8211; 15x<br \/>\nh = 300 &#8211; 15t \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =300 &#8211; 15(0) = 300 . co-ordinates are (0 , 300)<br \/>\nif x = 1 , then y = 300 &#8211; 15(1) = 285 . co-ordinates are (1 , 285)<br \/>\nif x = 2 , then y = 300 &#8211; 15(2) = 270\u00a0 , co-ordinates are (2 , 270)<br \/>\nif x = 3 , then y = 300 &#8211; 15(3) = 255\u00a0 , co-ordinates are (3 , 255)<br \/>\nThe co-ordinates (0 , 300) , (1 , 285) , (2 , 270) , (3 , 255) form a straight line .<\/p>\n<p>The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-71.png\" alt=\"\" width=\"220\" height=\"232\" \/><\/p>\n<p>Given , h = 300- 16t<sup>2<\/sup>\u00a0\u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =300- 16(0)<sup>2<\/sup>\u00a0 = 300 . co-ordinates are (0 , 300)<br \/>\nif x = 1 , then y =300- 16(1)<sup>2<\/sup> = 284 . co-ordinates are (1 , 284)<br \/>\nif x = 2 , then y = 300- 16(2)<sup>2<\/sup> = 236 , co-ordinates are (2 , 236)<br \/>\nif x = 3 , then y = 300- 16(3)<sup>2<\/sup> = 252\u00a0 , co-ordinates are (3 , 252)<br \/>\nThe co-ordinates (0 , 300) , (1 , 284) , (2 , 236) , (3 , 252) does not form a straight line .<\/p>\n<p>The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-72.png\" alt=\"\" width=\"218\" height=\"233\" \/><\/p>\n<p>b. For, h = 300 \u2013 15t , The graph is linear so the so it is a function,<br \/>\nFor h = 300- 16t<sup>2<\/sup> , The graph is linear so the so it is a function.<\/p>\n<p>c. Sky diver has the slow fall while compared to the bowling ball , because parachute can be controlled with the wind and can be divert the destination point, and bowling ball cannot be controlled while falling.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 2\" width=\"184\" height=\"88\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Does the table represent a linear or nonlinear function? Explain.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 3\" width=\"197\" height=\"71\" \/><br \/>\nAnswer: y = 2x &#8211; 12 is linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (2 , -8) , (4 , -4) , (6 , 0) , (8 , 4)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (6 ,0) and (8, 4)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (4 \u2013 0) \/ (8\u2013 6)<br \/>\nm = 4\/2<br \/>\nm = 2<br \/>\nsubstitute the slope in the (8 , 4) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny &#8211; 4 = 2 ( x &#8211; 8)<br \/>\ny &#8211; 4 = 2x &#8211; 16<br \/>\ny = 2x &#8211; 16 + 4<br \/>\ny = 2x &#8211; 12<br \/>\nSo ,\u00a0 y = 2x &#8211; 12 is linear function.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-4.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 4\" width=\"183\" height=\"66\" \/><br \/>\nAnswer: y = &#8211;\\(\\frac{5}{3}\\)x + 25 is linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (0 , 25) , (3 , 20) , (7 , 15) , (12 , 10)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (0 ,25) and (3, 20)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (20 \u2013 25) \/ (3\u2013 0)<br \/>\nm = -5\/3<br \/>\nBecause the line crosses the y axis at ( 0, 25 ) , The y intercept is 25.<br \/>\nSo , the linear function is y = &#8211;\\(\\frac{5}{3}\\)x + 25.<br \/>\nSo , y = &#8211;\\(\\frac{5}{3}\\)x + 25 is linear function.<\/p>\n<p><strong>Does the equation represent a linear or nonlinear function? Explain.<\/strong><br \/>\nQuestion 3.<br \/>\ny = x + 5<br \/>\nAnswer: y = x + 5 is a linear function<\/p>\n<p>Explanation:<br \/>\nGiven , y = x + 5\u00a0 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 + 5 = 5 . co-ordinates are (0 , 5)<br \/>\nif x = 1 , then y = 1 + 5 = 6 . co-ordinates are (1 , 6)<br \/>\nif x = 2 , then y = 2 + 5 = 7 , co-ordinates are (2 , 7)<br \/>\nThe co-ordinates (0 , 5) , (1 , 6) , (2 , 7) form a straight line .<br \/>\nEach x input has only one y output so it is a function .<br \/>\nAnd it\u00a0 forms a straight line when graphed .<br \/>\nSo, y = x + 5 is a linear function.<\/p>\n<p>Question 4.<br \/>\ny = \\(\\frac{4x}{3}\\)<br \/>\nAnswer: y = \\(\\frac{4x}{3}\\) is a linear function.<\/p>\n<p>Explanation:<br \/>\nGiven , y = \\(\\frac{4x}{3}\\) , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = \\(\\frac{4(0)}{3}\\) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = \\(\\frac{4(1)}{3}\\) = \\(\\frac{4}{3}\\)\u00a0 = 1.3. co-ordinates are (1 , 1.3)<br \/>\nif x = 2 , then y = \\(\\frac{4(2)}{3}\\) = \\(\\frac{8}{3}\\) = 2.6 , co-ordinates are (2 , 2.6)<br \/>\nThe co-ordinates (0 , 0) , (1 ,1.3 ) , (2 , 2.6) form a straight line .<br \/>\nEach x input has only one y output so it is a function .<br \/>\nAnd it forms a straight line when graphed .<br \/>\nSo, y = \\(\\frac{4x}{3}\\) is a linear function.<\/p>\n<p>Question 5.<br \/>\ny = 1 &#8211; x<sup>2<\/sup><br \/>\nAnswer: y = 1 &#8211; x<sup>2<\/sup> is not a linear function.<\/p>\n<p>Explanation:<br \/>\nGiven , y = 1 &#8211; x<sup>2<\/sup> \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 1 &#8211; 0<sup>2<\/sup> = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = 1 &#8211; 1<sup>2<\/sup> = 0 . co-ordinates are (1 , 0)<br \/>\nif x = 2 , then y = 1 &#8211; 2<sup>2<\/sup> = -3 , co-ordinates are (2 , -3)<br \/>\nThe co-ordinates (0 , 5) , (1 , 6) , (2 , 7) form a straight line .<br \/>\nEach x input has only one y output so it is a function .<br \/>\nAnd it does not forms a straight line when graphed .<br \/>\nSo, y = 1 &#8211; x<sup>2<\/sup> is not a linear function.<\/p>\n<p><strong>Does the graph represent a linear or nonlinear function? Explain.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 5\" width=\"140\" height=\"150\" \/><br \/>\nAnswer: The graph represents a nonlinear function.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , 2) , (-1 , 0) ,\u00a0 (-2 , -2 ) , (-3 , -4), (0 , 1 ) , (2 , -2) , ( 3, -4 )<br \/>\nThe inputs have more than one output ,<br \/>\nAnd points form a straight line<br \/>\nSo , the graph is non linear function<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 6\" width=\"147\" height=\"146\" \/><br \/>\nAnswer: The graph is a linear function<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , 0) , (-1 , -1) ,\u00a0 (-2 , -2 ) , (-3 , -3), (1 , 1 ) , (2 , 2) , ( 3, 3 )<br \/>\nThe inputs have exactly one output ,<br \/>\nAnd points form a straight line<br \/>\nSo , the graph is a linear function.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>IDENTIFYING FUNCTIONS<\/strong> Does the table or graph represent a linear or nonlinear function? Explain.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 7\" width=\"191\" height=\"74\" \/><br \/>\nAnswer: It is not a linear function<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (3 , 0) , (-1 , 2) , (-5 , 4) , (-9 , 6)<br \/>\nEach input has exactly one output<br \/>\nand it does not form a straight line when graphed<br \/>\nSo, it is not a linear function .<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 8\" width=\"141\" height=\"138\" \/><br \/>\nAnswer: The graph is non linear function<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , -1) , (-1 , 0) ,\u00a0 (-2 , 3 ) , (1 , 0 ) , (2 , 3) .<br \/>\nThe inputs have exactly one output ,<br \/>\nAnd points does not form a straight line<br \/>\nSo , the graph is non linear function<\/p>\n<p>Question 10.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 9\" width=\"377\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-9.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-9-300x42.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer: 5xy = -2 does not belong with the other three.<\/p>\n<p>Explanation:<br \/>\n15y = 6x , y = \\(\\frac{2}{5}\\)x , 10y = 4x .<br \/>\nThese are evaluated as 5y = 2x<br \/>\n5xy = -2 , is different from 5y = 2x.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 11.<br \/>\nThe loudness of sound is measured in (dB). The graph shows the loudness y of a sound (in decibels) x meters from the source of the sound. Is the relationship between loudness and distance linear or nonlinear? Approximate the loudness of the sound 12 meters from the source.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 10\" width=\"147\" height=\"229\" \/><br \/>\nAnswer: The relationship between loudness and distance\u00a0 is nonlinear Function. And the loudness of the sound 12 meters from the source is approximately 85dB as shown in the graph.<\/p>\n<p>Explanation:<br \/>\nAs shown in the graph , the plot of the points does not form a straight line ,<br \/>\nIts a parabolic decay , The amount of loudness decreases with the increase in distance,<br \/>\nSo, The relationship between loudness and distance\u00a0 is nonlinear Function.<\/p>\n<p>And the loudness of the sound 12 meters from the source is approximately 85dB as shown in the graph.<\/p>\n<p>Question 12.<br \/>\nA video blogger is someone who records a video diary. A new website currently hosts 90 video bloggers and projects a gain of 10 video bloggers per month. The table below shows the actual numbers of video bloggers. How does the projection differ from the actual change?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 11\" width=\"377\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-11.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-11-300x59.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer: Projections are more than the actual values<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-51800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-37.png\" alt=\"\" width=\"627\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-37.png 627w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-37-300x66.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><br \/>\nSo, Projections are more than the actual values<\/p>\n<h3><a id=\"Comparing _Linear _and _Non _Linear _Functions _Homework _&amp; _Practice _7.4\"><\/a>Comparing Linear and Non Linear Functions Homework &amp; Practice 7.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write a linear function that relates y to x.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-12.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 12\" width=\"150\" height=\"141\" \/><br \/>\nAnswer: The linear function is y = x &#8211; 2<\/p>\n<p>In order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , -2) , (1 , -1 ) , (-1 , -3) , ( 2, 0), (3 , 1) , (4 , 2) , ( 5, 3)<br \/>\nFirst find the slope m of the line containing the two given points (2 ,0) and (3, 1)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (1 \u2013 0) \/ (3 \u2013 2)<br \/>\nm = 1 .<br \/>\nBecause the line crosses the y axis at ( 0, -2 ) , The y intercept is -2.<br \/>\nSo , the linear function is y = x &#8211; 2 .<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-13.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 13\" width=\"206\" height=\"71\" \/><br \/>\nAnswer: The linear function is y =\\(\\frac{-1}{1.5}\\)x + 5.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (0 , 5) , (1.5 , 4) , (3 , 3) , (4.5 , 2)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (1.5 ,4) and (3, 3)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (3 \u2013 4) \/ (3 \u2013 1.5)<br \/>\nm = -1 \/1.5<br \/>\nBecause the line crosses the y axis at ( 0, 5 ) , The y intercept is 5.<br \/>\nSo , the linear function is y =\\(\\frac{-1}{1.5}\\)x + 5.<\/p>\n<p>The vertices of a figure are given. Draw the figure and its image after a dilation with the given scale factor. Identify the type of dilation.<br \/>\nQuestion 3.<br \/>\nA (- 3, 1), B (- 1, 3), C (- 1, 1); k = 3<br \/>\nAnswer: The New right angle triangle is larger than the original one So , its a increase .<\/p>\n<p>Explanation:<br \/>\nGiven , (- 3, 1),\u00a0 (- 1, 3),\u00a0 (- 1, 1) these pairs form a right angle triangle<br \/>\nK = 3 , For the dilation figure multiply the 3 with the given ordered pairs , then<br \/>\n(- 3, 1) \u00d7 3 = ( -9 , 3)<br \/>\n(- 1, 3) \u00d7 3 = ( -3 , 9)<br \/>\n(- 1, 1) \u00d7 3 = (-3 , 3)<br \/>\nFrom these new ordered pairs we form a new\u00a0 right angle triangle<br \/>\nThe figure is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-38.png\" alt=\"\" width=\"631\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-38.png 631w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-38-300x228.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><br \/>\nThe New right angle triangle is larger than the original one So , its a increase .<\/p>\n<p>Question 4.<br \/>\nJ (2, 4), K (6, 10), L (8, 10), M (8, 4); k = \\(\\frac{1}{4}\\)<br \/>\nAnswer: It is a reduction<\/p>\n<p>Explanation:<br \/>\nGiven , (2, 4),\u00a0 (6, 10),\u00a0 (8, 10) ,(8,4) these pairs forms a figure<br \/>\nK = 0.25 , For the dilation figure multiply the 3 with the given ordered pairs , then<br \/>\n(2, 4) \u00d7 0.25 = (0.5, 1)<br \/>\n(6, 10) \u00d7 0.25 = (1.5, 2.5)<br \/>\n(8, 10) \u00d7 0.25 = (2, 2.5)<br \/>\n(8, 4) \u00d7 0.25 = (2 , 1)<br \/>\nFrom these new ordered pairs we form a new figure<br \/>\nThe figure is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-39.png\" alt=\"\" width=\"675\" height=\"406\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-39.png 675w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-39-300x180.png 300w\" sizes=\"(max-width: 675px) 100vw, 675px\" \/><br \/>\nThe New figure is smaller than the original , So, It is a reduction .<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>COMPARING FUNCTIONS<\/strong> Graph each equation. Decide whether each graph represents a linear or nonlinear function. (See Exploration 1, p. 295.)<br \/>\nQuestion 5.<br \/>\nh = 5 + 6t Equation 1<br \/>\nh = 5 + 6t<sup>2<\/sup> Equation 2<br \/>\nAnswer: h = 5 + 6t Equation 1 is a linear function<br \/>\nh = 5 + 6t<sup>2<\/sup> Equation 2 is a non linear function .<\/p>\n<p>Explanation:<br \/>\nGiven , h = 5 + 6t \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 5 + 6(0) = 5 . co-ordinates are (0 , 5)<br \/>\nif x = 1 , then y = 5 + 6(1) = 11 . co-ordinates are (1 , 11)<br \/>\nif x = 2 , then y = 5 + 6(2) = 17 , co-ordinates are (2 , 17)<br \/>\nif x = 3 , then y = 5 + 6(3) = 23 , co-ordinates are (3 , 23)<br \/>\nThe co-ordinates (0 , 5) , (1 , 11) , (2 , 17) , (3 , 23) form a straight line .<\/p>\n<p>Given , h = 5 + 6t<sup>2<\/sup> \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 5 + 6(0)\u00b2 = 5 . co-ordinates are (0 , 5)<br \/>\nif x = 1 , then y = 5 + 6(1)\u00b2 = 11 . co-ordinates are (1 , 11)<br \/>\nif x = 2 , then y = 5 + 6(2)\u00b2 = 26 , co-ordinates are (2 , 26)<br \/>\nif x = 3 , then y = 5 + 6(3)\u00b2 = 59 , co-ordinates are (3 , 59)<br \/>\nThe co-ordinates (0 , 5) , (1 , 11) , (2 , 26) , (3 , 59) does not form a straight line .<\/p>\n<p>The graph of both equations is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-40.png\" alt=\"\" width=\"621\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-40.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-40-300x194.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><br \/>\nSo, h = 5 + 6t Equation 1 is a linear function<br \/>\nh = 5 + 6t<sup>2<\/sup> Equation 2 is a non linear function .<\/p>\n<p>Question 6.<br \/>\ny = &#8211; \\(\\frac{x}{3}\\) Equation 1<br \/>\ny = &#8211; \\(\\frac{3}{x}\\) Equation 2<br \/>\nAnswer:\u00a0 y = &#8211; \\(\\frac{x}{3}\\) Equation 1 is a linear function<br \/>\ny = &#8211; \\(\\frac{3}{x}\\) Equation 2 is a non linear function.<\/p>\n<p>Given , y =- \\(\\frac{x}{3}\\) , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =- \\(\\frac{0}{3}\\) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = &#8211; \\(\\frac{1}{3}\\) = &#8211; 0.3 . co-ordinates are (1 , &#8211; 0.3 )<br \/>\nif x = 2 , then y = &#8211; \\(\\frac{2}{3}\\) = &#8211; 0.6 , co-ordinates are (2 ,-0.6)<br \/>\nif x = 3 , then y = &#8211; \\(\\frac{3}{3}\\) = -1 , co-ordinates are (3 , -1)<br \/>\nThe co-ordinates (0 , 0) , (1 , -0.3) , (2 , -0.6) , (3 , -1) form a straight line .<\/p>\n<p>Given , y =- \\(\\frac{3}{x}\\) , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =- \\(\\frac{3}{0}\\) = no number<br \/>\nif x = 1 , then y = &#8211; \\(\\frac{3}{1}\\) = &#8211; 3 . co-ordinates are (1 , &#8211; 1 )<br \/>\nif x = 2 , then y = &#8211; \\(\\frac{3}{2}\\) = &#8211; 1.5 , co-ordinates are (2 ,-1.5)<br \/>\nif x = 3 , then y = &#8211; \\(\\frac{3}{3}\\) = -1 , co-ordinates are (3 , -1)<br \/>\nThe co-ordinates (1 , -1) , (2 , -1.5) , (3 , -1) form a straight line .<\/p>\n<p>The graph of both the equations is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41.png\" alt=\"\" width=\"588\" height=\"367\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41-300x187.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\nSo,\u00a0 y = &#8211; \\(\\frac{x}{3}\\) Equation 1 is a linear function<br \/>\ny = &#8211; \\(\\frac{3}{x}\\) Equation 2 is a non linear function.<\/p>\n<p><strong>IDENTIFYING FUNCTIONS FROM TABLES<\/strong> Does the table represent a linear or nonlinear function? Explain.<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-14.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 14\" width=\"207\" height=\"68\" \/><br \/>\nAnswer:\u00a0 linear function is y = 4x + 4.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (0 , 4) , (1 , 8) , (2 , 12) , (3 , 16)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (2 , 12) and (3 , 16)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (16 \u2013 12) \/ (3\u2013 2)<br \/>\nm = 4\/1<br \/>\nm = 4<br \/>\nBecause the line crosses the y axis at ( 0, 4 ) , The y intercept is 4.<br \/>\nSo , the linear equation is y = 4x + 4.<br \/>\nAnd it is a linear function.<\/p>\n<p>The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-42.png\" alt=\"\" width=\"436\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-42.png 436w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-42-300x260.png 300w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-15.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 15\" width=\"200\" height=\"71\" \/><br \/>\nAnswer: y = 4x \u2013 6 is linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (6 , 21) , (5 , 15) , (4 , 10) , (3 , 6)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (4 , 10) and (3 , 6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6 \u2013 10) \/ (3\u2013 4)<br \/>\nm = -4\/-1<br \/>\nm = 4<br \/>\nsubstitute the slope in the(4 , 10) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 10 = 4 ( x \u2013 4)<br \/>\ny \u2013 10 = 4x \u2013 16<br \/>\ny = 4x \u2013 16 + 10<br \/>\ny = 4x \u2013 6<br \/>\nSo ,\u00a0 y = 4x \u2013 6 is linear function.<\/p>\n<p>The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-51842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-43.png\" alt=\"\" width=\"443\" height=\"382\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-43.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-43-300x259.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p><strong>IDENTIFYING FUNCTIONS FROM EQUATIONS<\/strong> Does the equation represent a linear or nonlinear function? Explain.<br \/>\nQuestion 9.<br \/>\n2x + 3y = 7<br \/>\nAnswer: The function is linear when m = \\(\\frac{-2}{3}\\) and c = \\(\\frac{7}{3}\\)<\/p>\n<p>Explanation:<br \/>\nGiven ,2x + 3y = 7<br \/>\n3y = 7 &#8211; 2x<br \/>\ny = \\(\\frac{-2}{3}\\)x+ \\(\\frac{7}{3}\\)<br \/>\nSo, The function is linear when m = \\(\\frac{-2}{3}\\) and c = \\(\\frac{7}{3}\\)<\/p>\n<p>Question 10.<br \/>\ny + x = 4x + 5<br \/>\nAnswer: The function is linear when m = 3 and c = 5 .<\/p>\n<p>Explanation:<br \/>\nGiven , y + x = 4x + 5<br \/>\ny = 4x &#8211; x + 5<br \/>\ny = 3x + 5<br \/>\nSo, The function is linear when m = 3 and c = 5 .<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{8}{x^{2}}\\)<br \/>\nAnswer: The function is linear when m = 8 and c = 0 .<\/p>\n<p>Explanation:<br \/>\nGiven , y = \\(\\frac{8}{x^{2}}\\)<br \/>\nslope m = 8<br \/>\nc = 0<br \/>\nSo, The function is linear when m = 8 and c = 0 .<\/p>\n<p><strong>IDENTIFYING FUNCTIONS FROM GRAPHS<\/strong> Does the graph represent a linear or nonlinear function? Explain.<br \/>\nQuestion 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-16.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 16\" width=\"177\" height=\"153\" \/><br \/>\nAnswer: The graph is linear function<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , 1) , (2 , 0) ,\u00a0 (4 , -1 ) , (-2 , 2), ( -4, 3 )<br \/>\nThe inputs have exactly one output ,<br \/>\nAnd points form a straight line<br \/>\nSo , the graph is linear function<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-17.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 17\" width=\"177\" height=\"162\" \/><br \/>\nAnswer: The graph is non linear function.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , 0) , (-1 , -1) ,\u00a0 (-4 , -2 ) , (1 , 1), ( 4, 2 )<br \/>\nThe inputs have exactly one output ,<br \/>\nAnd points does not form a straight line<br \/>\nSo , the graph is non linear function<\/p>\n<p>Question 14.<br \/>\n<strong>IDENTIFYING A FUNCTION<\/strong><br \/>\nThe graph shows the volume V (in cubic feet) of a cube with an edge length of x feet. Does linear nonlinear the graph represent a linear or nonlinear function? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-18.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 18\" width=\"168\" height=\"183\" \/><br \/>\nAnswer: The graph is non linear function<\/p>\n<p>n order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (1 , 1) , (2 , 8) ,\u00a0 (3 , 27 ) , (4 , 64)<br \/>\nThe inputs have exactly one output ,<br \/>\nAnd points does not form a straight line<br \/>\nSo , the graph is non linear function<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe frequency y (in terahertz) of a light wave is a function of its wavelength x (in nanometers). Is the function relating the wavelength of light to its frequency linear or nonlinear?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-19.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 19\" width=\"492\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-19.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-19-300x78.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\nAnswer: The function is a non linear function<\/p>\n<p>Explanation:<br \/>\ntable is as follows <img loading=\"lazy\" class=\"alignnone size-full wp-image-51852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-44.1.png\" alt=\"\" width=\"389\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-44.1.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-44.1-300x89.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\nchange in x is constant but change in y is not constant , it is increasing<br \/>\nSo, the function is a non linear function .<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe table shows the cost (in dollars) of pounds of sun flower seeds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-20.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 20\" width=\"149\" height=\"108\" \/><br \/>\na. What is the missing -value that makes the table represent a linear function?<br \/>\nb. Write a linear function that represents the cost of x pounds of seeds. Interpret the slope.<br \/>\nc. Does the function have a maximum value? Explain your reasoning.<br \/>\nAnswer:\u00a0 a. 3 pounds = $4.2<br \/>\nb. y = 1.4x\u00a0 is linear function.<br \/>\nc. \u00a0If y has maximum value then the x also has maximum value.<\/p>\n<p>Explanation:<br \/>\na. As per the table 1 pound = $1.4<br \/>\n2 pounds = $2.8<br \/>\n3pounds = $4.2<br \/>\n4 pounds = $5.6<br \/>\nSo, the price is increasing with weight of the seeds.<\/p>\n<p>b. Ordered pairs are (2 , 2.8) , (3 , 4.2) , (4 , 5.6)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (3 , 4.2) and (4 , 5.6)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (5.6 \u2013 4.2) \/ (4 \u2013 3)<br \/>\nm = 1.4<br \/>\nsubstitute the slope in the (3 , 4.2) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 4.2 = 1.4 ( x \u2013 3)<br \/>\ny \u2013 4.2 = 1.4x \u2013 4.2<br \/>\ny = 1.4x \u2013 4.2 + 4.2<br \/>\ny = 1.4x<br \/>\nSo ,\u00a0 y = 1.4x\u00a0 is linear function.<\/p>\n<p>c. As shown in the table , and the function if y increases then x also increases with respect to the y<br \/>\nSo, if y has maximum value then the x also has maximum value.<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA birch tree is 9 feet tall and grows at a rate of 2 feet per year. The table shows the height h (in feet) of a willow tree after x years.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-7.4-21.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions 7.4 21\" width=\"173\" height=\"134\" \/><br \/>\na. Does the table represent a linear or nonlinear function? Explain.<br \/>\nb. Which tree is taller after 10 years? Explain.<br \/>\nAnswer: There is no linear relationship between x and y .<\/p>\n<p>Explanation:<br \/>\nTable is as follows <img loading=\"lazy\" class=\"alignnone size-full wp-image-51853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-45.png\" alt=\"\" width=\"382\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-45.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-45-300x96.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nChange in y is constant but change in x is increasing , not a constant<br \/>\nHence, there is no linear relationship between x and y .<\/p>\n<p>Question 18.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn their first year, Show A has 7 million viewers and Show B has 5 million viewers. Each year, Show A has 90% of the viewers it had in the previous year. Show B loses 200,000 viewers each year.<br \/>\na. Determine whether the function relating the year to the number of viewers is linear or nonlinear for each show.<br \/>\nb. Which show has more viewers in its sixth year?<br \/>\nAnswer: a. The function relating the year to the number of viewers is linear<br \/>\nb. Both shows\u00a0 has same number of viewers in the sixth year .<\/p>\n<p>Explanation:<br \/>\na. Given, In their first year, Show A has 7 million viewers and Show B has 5 million viewers. Each year, Show A has 90% of the viewers it had in the previous year. Show B loses 200,000 viewers each year.<br \/>\nFor show A<br \/>\nSo , In first year = 7<br \/>\n2 year = 90% of 7 = 6.3<br \/>\n3 year = 90% of 6.3 = 5.6<br \/>\n4 year = 90% of 5.6 = 5.04<br \/>\n5 year = 90% of 5 = 4.5<br \/>\n6 year = 90% of 4.5 = 4.05<br \/>\nSo the ordered pairs are (1 , 7) , (2 , 6.3) , (3 , 5.6) , (4 , 5), (5 , 4.5) , (6 , 4)<\/p>\n<p>For show B<br \/>\nIn first year = 5 , As the viewers reduces by 2,00,000 in 5M<br \/>\n2 year = 5 &#8211; 0.2 = 4.8<br \/>\n3 year = 4.8 &#8211; 0.2 = 4.6<br \/>\n4 year = 4.6 &#8211; 0.2 = 4.4<br \/>\n5 year = 4.4 &#8211; 0.2 = 4.2<br \/>\n6 year = 54.2 &#8211; 0.2 = 4<br \/>\nSo the ordered pairs are (1 , 5) , (2 , 4.8) , (3 , 4.6) , (4 , 4.4), (5 , 4.2) , (6 , 4)<br \/>\nAs the year increases the viewers are also decreasing constantly as per the individual shows<br \/>\nSo, The function relating the year to the number of viewers is linear .<\/p>\n<p>b. As shown in part a , the ordered pairs having (6,4) represents the number of viewers to the year<br \/>\nSo, Both shows\u00a0 has same number of viewers in the sixth year .<\/p>\n<p>Question 19.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe ordered pairs represent a function. (0,- 1), (1, 0), (2, 3), (3, 8), and (4, 15)<br \/>\na. Graph the ordered pairs and describe the pattern. Is the function linear or nonlinear?<br \/>\nb. Write an equation that represents the function.<br \/>\nAnswer: a. The graph is shown below and function is linear<br \/>\nb. The linear equation is y = 7x &#8211; 1.<\/p>\n<p>Explanation:<br \/>\nGiven, ordered pairs represent a function. (0,- 1), (1, 0), (2, 3), (3, 8), and (4, 15)<br \/>\na. the graph is\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-51857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-46.png\" alt=\"\" width=\"437\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-46.png 437w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-46-300x263.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><br \/>\nEach input has exactly one output and it forms a straight line So, the graph is linear<br \/>\nb. First find the slope m of the line containing the two given points (3 ,8) and (4, 15)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (15 \u2013 8) \/ (4\u2013 3)<br \/>\nm = 7\/1<br \/>\nm = 7<br \/>\nBecause the line crosses the y axis at ( 0, -1 ) , The y intercept is -1.<br \/>\nSo , the linear equation is y = 7x &#8211; 1.<\/p>\n<h3><a id=\"Lesson _7.5 _Analyzing _and _Sketching _Graphs\"><\/a>Lesson 7.5 Analyzing and Sketching Graphs<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Matching Situations to Graphs<br \/>\nWork with a partner. Each graph shows your speed during a bike ride. Match each situation with its graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 1\" width=\"619\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-1.png 619w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-1-300x156.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><br \/>\na. You increase your speed, then ride at a constant speed along a bike path. You then slow down until you reach your friend\u2019s house. Analyze Relationships<br \/>\nb. You increase your speed, then go down a hill. You then quickly come to a stop at an intersection.<br \/>\nc. You increase your speed, then stop at a store for a couple of minutes. You then continue to ride, increasing your speed.<br \/>\nd. You ride at a constant speed, then go up a hill. Once on top of the hill, you increase your speed.<br \/>\nAnswer: a &#8211; C ,<br \/>\nb &#8211; A ,<br \/>\nc &#8211; D ,<br \/>\nd &#8211; B ,<\/p>\n<p>Explanation:<br \/>\na. You increase your speed, then ride at a constant speed along a bike path. You then slow down until you reach your friend\u2019s house. The graph C has the perfect graph representing the situation of given question.<br \/>\nb. You increase your speed, then go down a hill. You then quickly come to a stop at an intersection.<br \/>\nBecause The graph A has the bike speed representing the situation for the time .<br \/>\nc. You increase your speed, then stop at a store for a couple of minutes. You then continue to ride, increasing your speed. Thus, The graph D is the final answer for the question<br \/>\nd. You ride at a constant speed, then go up a hill. Once on top of the hill, you increase your speed.<br \/>\nBecause of the speed with respect to time the graph B is the correct answer for the question.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Interpreting a Graph<br \/>\nWork with a partner. Write a short paragraph that describe show the height changes over time in the graph shown. What situation can this graph represent?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 2\" width=\"178\" height=\"137\" \/><br \/>\nAnswer: The Graph can be representing a situation for low and high tides of the Ocean<\/p>\n<p>Explanation:<br \/>\nAs shown in the figure, The graph is plotted between the height and time,<br \/>\nWe can take an example of an Ocean for its waves , As the time passes at the morning of a normal day, The waves of the ocean start rising higher at a period of time, and for the time being maintaining a peak height then drops to a lower height at a particular intervals of time , this process takes place for a while and vise versa.<br \/>\nThus, the Graph can be representing a situation for low and high tides of the Ocean<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nThe graph shows the location of a pelican relative to your location.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 3\" width=\"163\" height=\"159\" \/><br \/>\na. Describe the path of the pelican.<br \/>\nb. Write an explanation for the decrease in the vertical distance of the pelican.<br \/>\nAnswer: Both of them are explained below.<\/p>\n<p>Explanation:<br \/>\na. The path of the pelican is flying in the air , As they always fly in line and the amazing thing is the deeper the prey the higher they dive.<br \/>\nThe graph shows the relationship between the horizontal distance that is the height from the land, vertical distance is the point from where its destination point is located, so at the starting point of the flight it has more distance from the ground means flying at a higher level , as the time passes it reaches to the closer point of its destination point so the altitude of the flight decreases with the decrease in the vertical distance and at a particular distance reaches its point of destination.<\/p>\n<p>b. The decrease in the vertical distance of the pelican. is due to its flight to the destination point as it requires to stop flying to reach it, so in order to have a smooth landing on the ground , the bird gradually decreases its speed by decreasing its altitude.<\/p>\n<p>Question 2.<br \/>\nA fully-charged battery loses its charge at a constant rate until it has no charge left. You plug it in, and it fully recharges at a constant rate. Then it loses its charge at a constant rate until it has no charge left. Sketch a graph that represents this situation.<br \/>\nAnswer:\u00a0 The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-47.png\" alt=\"\" width=\"512\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-47.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-47-300x159.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Explanation:<br \/>\nIn the graph , let the x-axis be time and y-axis be the battery charge ,<br \/>\nA fully-charged battery loses its charge at a constant rate until it has no charge left. So, line segment starts from 100 and decreases until it touches the x-axis.<br \/>\nYou plug it in, and it fully recharges at a constant rate. Thus, line segment increases at a constant rate until it reaches 100<br \/>\nThen it loses its charge at a constant rate until it has no charge left. line segment decreases again at a constant rate until it again touches the x-axis .<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>ANALYZING GRAPHS<\/strong><br \/>\nThe graph shows the growth rate of a plant over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 4\" width=\"163\" height=\"156\" \/><br \/>\na. Describe the change in growth rate.<br \/>\nb. Write an explanation for the decrease in growth rate and the increase in growth rate.<br \/>\nAnswer: the answers are given below<\/p>\n<p>Explanation:<br \/>\na. the change in growth rate of a plant over the time is given by its size and height , So as the time passes the growth rate is constant from the the start and from a particular time the growth rate has been dropping slightly due to external or internal reasons of a plant and again at some time the growth rate is increasing at a constant rate until it reaches to its perfect growth of a plant.<\/p>\n<p>b. The decrease in growth rate of the plant is due to some external causes like weather, rain, sunlight , watering, and the soil may effect its growth rate and the increase in growth rate is probably due to its soil fertility and sufficient sunlight providing sufficient chlorophyll.<\/p>\n<p>Question 4.<br \/>\n<strong>SKETCHING GRAPHS<\/strong><br \/>\nAs you snowboard down a hill, you gain speed at a constant rate. You come to a steep section of the hill and gain speed at a greater constant rate. You then slow down at a constant rate until you come to a stop. Sketch a graph that represents this situation.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-48.png\" alt=\"\" width=\"508\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-48.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-48-300x159.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Explanation:<br \/>\nIn the graph , let the x-axis be time and y-axis be the speed ,<br \/>\nAs you snowboard down a hill, you gain speed at a constant rate, line segment decreases at a constant rate<br \/>\nYou come to a steep section of the hill and gain speed at a greater constant rate, line segment becomes steeper i.e., the line segment decreases at a high constant rate.<br \/>\nYou then slow down at a constant rate until you come to a stop, line segment becomes flatter i.e., the constant rate of decrease becomes less until it touches its x-axis<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\nTwo rowing teams are in a race. The graph shows their distances from the finish line over time. Describe the speed of each team throughout the race. Then determine which team finishes first.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 5\" width=\"166\" height=\"159\" \/><br \/>\nAnswer: Team B will finishes race first.<\/p>\n<p>Explanation:<br \/>\nTeam A , The relationship between the time and distance from the finish line is given in the graph,<br \/>\nAt starting point Team A has maintained a fair speed at the Beginning of the race and has been a little slow while reaching out to the destination point, and for a while they have been balancing the speed with the distance representing a curving point in the graph and directly dropping to the finish line drastically creating a slope, until it reaches in the x-axis line.<br \/>\nTeam B , The relationship between the time and distance from the finish line is given in the graph,<br \/>\nAs same as the Team A , Team B has a perfect start but it has been a way different them Team A because Team B has a game plan to win the race, as shown in the graph they have maintained a constant speed while reaching out to the destination and also having a smooth drift at a level of decreasing their distance from the finish line.<\/p>\n<p>Team B will\u00a0 finishes the race first because they are having a constant and smooth decreasing speed which comes to an end gradually at the finishing line.<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe graphs show the movements of two airplanes over time. Describe the movement of each airplane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 6\" width=\"444\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-6.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-6-300x120.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><br \/>\nAnswer: Detailed explanation is given below.<\/p>\n<p>Explanation:<br \/>\nAs shown in the graph , x-axis is time and y-axis be the height above ground<br \/>\nAirplane A, the line segment at a constant rate at the time of starting of the takeoff and then drops to a point while decreasing in the height to the ground for landing and for a constant time it is at the ground level until again it takes off\u00a0 having an increase in the height from the ground level , at last it maintains a constant speed.<\/p>\n<p>Airplane B, the line segment at a constant rate at the time of starting of the takeoff and then drops to a point while decreasing in the height to the ground for landing and for a constant time it is at the ground level until again it takes off\u00a0 having an increase in the height from the ground level , at last it maintains a constant speed.<br \/>\nIt is as same as the airplane A.<\/p>\n<h3><a id=\"Analyzing _and _Sketching _Graphs _Homework _&amp; _Practice _7.5\"><\/a>Analyzing and Sketching Graphs Homework &amp; Practice 7.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Does the table or equation represent a linear or nonlinear function? Explain.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 7\" width=\"194\" height=\"72\" \/><br \/>\nAnswer: y = -0.5x + 11.5 is a linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (-5 , 14) , (-1 , 12) , (3 , 10) , (7 , 8)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (3 , 10) and (7 , 8)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (8 \u2013 10) \/ (7 \u2013 3)<br \/>\nm = -2\/4<br \/>\nm = -0.5<br \/>\nsubstitute the slope in the(3 , 10) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 10 = -0.5 ( x \u2013 3)<br \/>\ny \u2013 10 = -0.5x + 1.5<br \/>\ny = -0.5x + 1.5 + 10<br \/>\ny = -0.5x + 11.5<br \/>\nSo , the linear equation is y = -0.5x + 11.5<br \/>\nAnd it is a linear function.<\/p>\n<p>The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-49.png\" alt=\"\" width=\"604\" height=\"386\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-49.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-49-300x192.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 2.<br \/>\ny = x<sup>2<\/sup> + 8<br \/>\nAnswer: The function is linear\u00a0 when m= 1 and c = 8.<\/p>\n<p>Explanation:<br \/>\nGiven , y = x<sup>2<\/sup> + 8 ,<br \/>\nslope m = 1<br \/>\nc = 8<br \/>\nSo, the function is linear when m = 1 and c= 8.<\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 3.<br \/>\n&#8211; 4x + y = &#8211; 1<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-52.png\" alt=\"\" width=\"660\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-52.png 660w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-52-300x215.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>Explanation:<br \/>\nwe can write &#8211; 4x + y = &#8211; 1 as y = 4x &#8211; 1<br \/>\nGiven , y = 4x &#8211; 1\u00a0 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 4(0) &#8211; 1 = -1 . co-ordinates are (0 , -1)<br \/>\nif x = 1 , then y = 4(1) &#8211; 1 = 3 . co-ordinates are (1 , 3)<br \/>\nif x = 2 , then y = 4(2) &#8211; 1 = 7 , co-ordinates are (2 , 7)<br \/>\nif x = 3 , then y = 4(3) &#8211; 1= 11 , co-ordinates are (3 , 11)<br \/>\nThe co-ordinates (0 , -1) , (1 , 3) , (2 , 7) , (3 , 11) form a straight line .<\/p>\n<p>Question 4.<br \/>\n2x &#8211; 3y = 12<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-50.png\" alt=\"\" width=\"547\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-50.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-50-300x230.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Explanation:<br \/>\nwe can write\u00a0 2x &#8211; 3y = 12 as y = \\(\\frac{2x-12}{3}\\) or y = \\(\\frac{2}{3}\\)x &#8211; 4<br \/>\nGiven , y =\\(\\frac{2}{3}\\)x &#8211; 4\u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = \\(\\frac{2}{3}\\)0 &#8211; 4= &#8211; 4 . co-ordinates are (0 , -4)<br \/>\nif x = 1 , then y = \\(\\frac{2}{3}\\)1 &#8211; 4 = 0.66 &#8211; 4 = -3.3 . co-ordinates are (1 , -3.3)<br \/>\nif x = 2 , then y = \\(\\frac{2}{3}\\)2 &#8211; 4 =0.66(2) &#8211; 4 =1.3 &#8211; 4 = -2.6, co-ordinates are (2 , -2.6)<br \/>\nif x = 3 , then y = \\(\\frac{2}{3}\\)3 &#8211; 4 = 0.66(3) &#8211; 4 = 1.98 &#8211; 4 = -2.0\u00a0 , co-ordinates are (3 , -2.0)<br \/>\nThe co-ordinates (0 , -4) , (1 , -3.3) , (2 , -2.6) , (3 , -2) form a straight line .<\/p>\n<p>Question 5.<br \/>\n5x + 10y = 30<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-54989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-51.png\" alt=\"\" width=\"460\" height=\"398\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-51.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-51-300x260.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Explanation:<br \/>\n5x + 10y = 30 can be written as y = -0.5x + 3<br \/>\ntake 5 common on both sides we get<br \/>\nx + 2y = 6<br \/>\ny = \\(\\frac{-x + 6}{2}\\)<br \/>\ny = \\(\\frac{-x}{2}\\) + 6<br \/>\ny = -0.5x + 3<br \/>\nGiven , y =-0.5x + 3 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = -0.5(0) + 3 = 3 . co-ordinates are (0 , 3)<br \/>\nif x = 1 , then y = -0.5(1) + 3= 2.5 . co-ordinates are (1 , 2.5)<br \/>\nif x = 2 , then y = -0.5(2) + 3 = 4 , co-ordinates are (2 , 4)<br \/>\nif x = 3 , then y = -0.5(3) + 3 = 4.5\u00a0 , co-ordinates are (3 , 4.5)<br \/>\nThe co-ordinates (0 , 3) , (1 , 2.5) , (2 , 4) , (3 , 4.5)does not form a straight line .<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>MATCHING DESCRIPTIONS WITH GRAPHS<\/strong> The graph shows your speed during a run. Match the verbal description with the part of the graph it describes. (See Exploration 1, p. 301.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 8\" width=\"216\" height=\"131\" \/><br \/>\nQuestion 6.<br \/>\nYou run at a constant speed.<br \/>\nAnswer: C<\/p>\n<p>Explanation:<br \/>\nBecause the line segment of the graph at point C show that the running speed is constant for a particular time ,<br \/>\nThus forming a straight horizontal line.<\/p>\n<p>Question 7.<br \/>\nYou slow down at a constant rate.<br \/>\nAnswer: D<\/p>\n<p>Explanation:<br \/>\nBecause the line segment of the graph at point D show that the running speed is decreasing at a constant rate for a particular time ,<br \/>\nThus forming a straight steep line down the time axis.<\/p>\n<p>Question 8.<br \/>\nYou increase your speed at a constant rate.<br \/>\nAnswer: A<\/p>\n<p>Explanation:<br \/>\nBecause the line segment of the graph at point A show that the running speed is increasing at a constant rate at a starting point of the race on time ,<br \/>\nThus forming a slope in the graph.<\/p>\n<p>Question 9.<br \/>\nYou increase your speed at a faster and faster rate.<br \/>\nAnswer: B<\/p>\n<p>Explanation:<br \/>\nBecause the line segment of the graph at point B show that the running speed is increasing at a faster rate after starting the race and maintaining a gradual growth of the speed and after reaching the next point speed is doubled from before ,<br \/>\nThus forming a slope with a curve in the graph.<\/p>\n<p><strong>ANALYZING GRAPHS<\/strong> Describe the relationship between the two quantities.<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 9\" width=\"150\" height=\"178\" \/><br \/>\nAnswer: As the Time passes there will be increase in the volume.<\/p>\n<p>Explanation:<br \/>\nThe graph shows the relation between the volume and time of a Balloon , To fill up the balloon with air, with the inlet of air increases in volume and the time taken to fill the balloon with air is shown ,<br \/>\nThe line segment starts at initial point stating the balloon at a no air state, then gradually increases with constant halts having constant volume at a particular time and vice versa.<\/p>\n<p>So, As the Time passes there will be increase in the volume.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 10\" width=\"171\" height=\"191\" \/><br \/>\nAnswer: As the times passes Dollars are maintaining imbalance.<\/p>\n<p>Explanation:<br \/>\nThe relationship between the time and dollars is given in the graph, As we all know money is never ever constant with time , As if it only increases or decreases or having both simultaneously , in this graph the line segment is having a steep and at some point of time it is maintaining a slight growth constantly with the time.<\/p>\n<p>So, As the times passes Dollars are maintaining imbalance.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 11\" width=\"190\" height=\"198\" \/><br \/>\nAnswer: An engine power is directly proportional to the engine speed and its horse power<\/p>\n<p>Explanation:<br \/>\nThe relationship between the engine speed and horse power is given in the graph, Generally every automobile is is defined as the best for its horse power which is the heart of the engine and it highlights the speed of the vehicle, Here engine power is defined by the horse power and the engine speed the line segment is having a curve increment in the horse power due to the increase in engine speed.<\/p>\n<p>So, An engine power is directly proportional to the engine speed and its horse power<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 12\" width=\"176\" height=\"190\" \/><br \/>\nAnswer: As time increases the process of grams decaying will be faster.<\/p>\n<p>Explanation:<br \/>\nThe relationship between grams and time is given in the graph, its obvious that every product has its own expiry date, and if it crosses that its starts to decay, the graph implies that with the increase time the quality of the gram decreases or grams start to decay . The line segment in the graph shows that the gradually decrease indicating the spoiling rate of the grams\u00a0 with rate of change of time.<\/p>\n<p>So, As time increases the process of grams decaying will be faster.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 13\" width=\"171\" height=\"195\" \/><br \/>\nAnswer: At the particular intervals of time hair growth has stopped and at regular intervals again starts growing with respect to the time.<\/p>\n<p>Explanation:<br \/>\nThe graph shows the relationship between the length of the hair and time taken to the growth of the hair, of course hair growth is not constant every time, here we have the graph with the line segment\u00a0 not constant and having breaks at the times of interval.<\/p>\n<p>So, At the particular intervals of time hair growth has stopped and at regular intervals again starts growing with respect to the time.<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 14\" width=\"195\" height=\"190\" \/><br \/>\nAnswer: In a period of time the balance will be reduced gradually at regular intervals maintaining a constant balance to clear the loan.<\/p>\n<p>Explanation:<br \/>\nThe relationship between the balance of the loan with the time period of the loan to be cleared, The loan should be cleared in the time limit and should maintain a neat balance, every increase in time period the balance is debited from the loan , there will be decrease in the balance and gaps are occurred in the graph.<\/p>\n<p>so, In a period of time the balance will be reduced gradually at regular intervals maintaining a constant balance to clear the loan.<\/p>\n<p>Question 16.<br \/>\n<strong>ANALYZING GRAPHS<\/strong><br \/>\nWrite an explanation for the relationship shown in the graph in Exercise 10.<br \/>\nAnswer: The graph shows the relation between the volume and time of a Balloon , To fill up the balloon with air, with the inlet of air increases in volume and the time taken to fill the balloon with air is shown ,<br \/>\nThe line segment starts at initial point stating the balloon at a no air state, then gradually increases with constant halts having constant volume at a particular time and vice versa.<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe graph shows the natural gas usage for a house.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 15\" width=\"174\" height=\"143\" \/><br \/>\na. Describe the change in usage from January to March.<br \/>\nb. Describe the change in usage from March to May.<br \/>\nAnswer: a. The change in usage from January to March, As shown in the graph the usage is at peaks in the month of January and started to decrease after that month and continuing to decrease in the month of March.<br \/>\nb.\u00a0 The change in usage from March to May, As shown in the graph the usage is continuing to decrease in the month of March and started to increase again in the month of May and maintaining to use highly from the month of May.<\/p>\n<p>Explanation:<br \/>\na. The change in usage from January to March, As shown in the graph the usage is at peaks in the month of January and started to decrease after that month and continuing to decrease in the month of March.<\/p>\n<p>b.\u00a0 The change in usage from March to May, As shown in the graph the usage is continuing to decrease in the month of March and started to increase again in the month of May and maintaining to use highly from the month of May.<\/p>\n<p><strong>SKETCHING GRAPHS<\/strong> Sketch a graph that represents the situation.<br \/>\nQuestion 18.<br \/>\nThe value of a television decreases at a constant rate, and then remains constant.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-53.png\" alt=\"\" width=\"554\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-53.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-53-300x168.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Explanation:<br \/>\nDraw the axis and label the x- axis as time and y- axis as value, then sketch the graph,<br \/>\nThe value of the television decreases at a constant rate: line segment starts to decrease at a constant rate,<br \/>\nAnd then remains constant, after reaching a certain value : line segment becomes parallel to horizontal axis.<\/p>\n<p>Question 19.<br \/>\nThe distance from the ground changes as your friend swings on a swing.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-54.1.png\" alt=\"\" width=\"387\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-54.1.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-54.1-300x155.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Explanation:<br \/>\nYour friend starts close to the ground and then swings up. Then she falls back down close to the ground again and swings back . When she swings back, she gets higher than when she was swinging forward, she then starts to swing forward again getting close to the ground and then going up even higher than when she was swinging backward, she continues to getting higher and higher every time she swings forwards and backwards,<\/p>\n<p>Question 20.<br \/>\nThe value of a rare coin increases at a faster and faster rate.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-55.png\" alt=\"\" width=\"542\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-55.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-55-300x183.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Explanation:<br \/>\nDraw the Axis and label them as x-axis as time and y &#8211; axis as distance,<br \/>\nThe value of a rare coin increases at a faster and faster rate , so the curve moves upwards at an increasing rate.<\/p>\n<p>Question 21.<br \/>\nYou are typing at a constant rate. You pause to think about your next paragraph and then you resume typing at the same constant rate.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-56.png\" alt=\"\" width=\"265\" height=\"207\" \/><\/p>\n<p>Explanation:<br \/>\nA constant rate means that portion of the graph is linear , pausing means the number of words stays constant, typing again at the same constant rate means the last piece of the graph is linear again with the same slope as the first portion of the graph.<\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe graph shows the speed of an object over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 16\" width=\"171\" height=\"136\" \/><br \/>\na. Sketch a graph that shows the distance traveled by the object over time.<br \/>\nb. Describe a possible situation represented by the graphs.<br \/>\nAnswer: a. The distance and time are directly proportional to each other.<br \/>\nb. As time passes the speed and time are relatively balancing each other in the graph.<\/p>\n<p>Explanation:<br \/>\na. The graph is\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-55017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-57.png\" alt=\"\" width=\"398\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-57.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-57-300x268.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><br \/>\nIn this graph the relationship between distance and time is shown, for example , let the object be a bike, the time taken to reach the destination for the bike is directly proportional to the distance travelled , So as time passes the distance is gradually increasing from the starting point.<\/p>\n<p>So, the distance and time are directly proportional to each other.<\/p>\n<p>b. Th graph shown , is the relationship between the speed and the time , let the object moving be Train,<br \/>\nit is running between the station so it has to be halted in the stations to be listed in the stoppings , So the line segment is started with a constant speed with the time and again at the time interval dropping the speed with respect to time it has maintaining the same speed .<\/p>\n<p>So, As time passes the speed and time are relatively balancing each other in the graph.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe graph shows the average scores of two bowlers from the start of a season to the end of the season.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-17.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 17\" width=\"176\" height=\"168\" \/><br \/>\na. Describe each bowler\u2019s performance.<br \/>\nb. Who had a greater average score most of the season? Who had a greater average score at the end of the season?<br \/>\nc. Write an explanation for the change in each bowler\u2019s average score throughout the bowling season.<br \/>\nAnswer: All the answers are explained below<\/p>\n<p>Explanation:<br \/>\na.\u00a0 Bowler A : As the graph represent the relationship between the score and the week, bowler A has started with the good take off and having able to grasp the same energy his performance on the goals are increasing rapidly over the week and had the good score than Bowler B.<\/p>\n<p>Bowler B : As the graph represent the relationship between the score and the week, bowler B has started with the good take off but as the time passes the performance of the\u00a0 bowler is has been intended to decrease his scores gradually over the week.<\/p>\n<p>b. \u00a0Bowler A and Bowler B had a greater average score most of the season, but Bowler A had a greater average score at the end of the season<\/p>\n<p>c. Bowler A has the same energy his performance on the goals are increasing rapidly over the week and had the good score than Bowler B. so it has a smaller change in average&#8217;s score in the bowling season .<br \/>\nWhile Bowler B has good take off but as the time passes the performance of the\u00a0 bowler is has been intended to decrease his scores gradually over the week. so he has a drastic change in average&#8217;s score in the bowling season .<\/p>\n<p>Question 24.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou can use a supply and demand model to understand how the price of a product changes in a market. The supply curve of a particular product represents the quantity suppliers will produce at various prices. The demand curve for the product represents the quantity consumers are willing to buy at various prices.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-7-Functions-7.5-18.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 7 Functions 7.5 18\" width=\"196\" height=\"173\" \/><\/p>\n<p>a. Describe and interpret each curve.<br \/>\nb. Which part of the graph represents a surplus? Explain your reasoning.<br \/>\nc. The curves intersect at the equilibrium point, which is where the quantity produced equals the quantity demanded. Suppose that demand for a product suddenly increases, causing the entire demand curve to shift to the right. What happens to the equilibrium point?<br \/>\nAnswer:\u00a0 All of them are explained below .<\/p>\n<p>Explanation:<br \/>\na. The supply curve of a particular product represents the quantity suppliers will produce at various prices, As shown in the graph, the relationship between the price and quantity is given , so if prices increases gradually Quantity increases .<br \/>\nThe demand curve for the product represents the quantity consumers are willing to buy at various prices, As shown in the graph, the relationship between the price and quantity is given , so if prices decreases with increase in Quantity .<\/p>\n<p>b. The graph does not implies any surplus because each demand and supply is given by their respective curve over the prices and quantity<\/p>\n<p>c. As shown in the graph, The curves intersect at the equilibrium point, which is where the quantity produced equals the quantity demanded. Given, that demand for a product suddenly increases, causing the entire demand curve to shift to the right. Then the equilibrium point will be pointed where the two curves meet after the change in the demand graph so change in the supply graph is also possible.<\/p>\n<h3><a id=\"Functions _Connecting _Concepts\"><\/a>Functions Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nThe table shows the lengths x (in inches) and weights y(in pounds) of several infants born at a hospital. Determine whether weight is a function of length. Then estimate the weight of an infant that is 20 inches long.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cc 1\" width=\"175\" height=\"212\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know the lengths and weights of several infants. You are asked to determine whether weight is a function of length and to estimate the weight of a 20-inch-long infant.<\/p>\n<p>Make a plan.<br \/>\nDetermine whether any of the lengths are paired with more than one weight. Then use a graphing calculator to find an equation that represents the data. Evaluate the equation when x = 20 to estimate the weight of a 20-inch-long infant.<\/p>\n<p>Solve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer: Weight is the function of the length<\/p>\n<p>Explanation:<br \/>\nFrom the table we have , Each length has only one weight , so weight is a function of length.<br \/>\nFirst find the slope m of the line containing the two given points (19.3 , 7.3) and (18.9 , 6.5)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (6.5 \u2013 7.3) \/ (18.9 \u2013 19.3)<br \/>\nm = 0.2<br \/>\nsubstitute the slope in the (19.3 , 7.3) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 7.3 = 0.2 ( x \u2013 19.3)<br \/>\ny \u2013 7.3 = 0.2x \u2013 3.86<br \/>\ny = 0.2x \u2013 3.86 + 7.3<br \/>\ny = 0.2x + 3.4<br \/>\nSo ,\u00a0 y = 0.2x + 3.4 is linear function.<\/p>\n<p>For x = 20 ,<br \/>\ny = 0.2 (20) + 3.4<br \/>\ny = 4 + 3.4<br \/>\ny = 7.4<\/p>\n<p>So, The weight of an infant that is 20 inches long. is 7.4.<\/p>\n<p>Question 2.<br \/>\nEach mapping diagram represents a linear function. At what point do the graphs of the functions intersect? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cc 2\" width=\"370\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-2.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-2-300x133.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:\u00a0 The point of intersection is (-1, -4)<\/p>\n<p>Explanation:<br \/>\nFunction 1 &#8211; Ordered pairs are ( -8 , 24 ) , ( -3 , 4 ) , ( -1 , -4 ) , ( 1 , -12) .<br \/>\nFunction 2 &#8211; Ordered pairs are ( 6 , 17 ) , ( 10 , 29 ) , ( 13 , 38 ) , ( 15 , 44 ) .<br \/>\nGraph the points we get, <img loading=\"lazy\" class=\"alignnone size-full wp-image-55071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-58.png\" alt=\"\" width=\"888\" height=\"557\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-58.png 888w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-58-300x188.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-58-768x482.png 768w\" sizes=\"(max-width: 888px) 100vw, 888px\" \/> So, The point of intersection is (-1,-4).<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Heat Index<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cApparent Temperature.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cc 3\" width=\"367\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-3.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cc-3-300x148.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Functions _Chapter _Review\"><\/a>Functions Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 1\" width=\"560\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-1-300x40.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><br \/>\nInput: Ordered pairs can be used to show inputs and outputs , inputs are represented by x<\/p>\n<p>Output: Ordered pairs can be used to show inputs and outputs , Outputs are represented by y<\/p>\n<p>Relation: A relation pairs inputs with outputs<\/p>\n<p>Mapping diagram: A relation can be represented by ordered pairs or mapping diagrams.<\/p>\n<p>Function: The relation that pairs each input with exactly one output is a function.<\/p>\n<p>Function rule: it is an equation, that describes the relationship between inputs(independent variables) and outputs(dependent variables).<\/p>\n<p>Linear function: A linear function is a function whose graph is a straight line i.e., non vertical line . A linear can be written in the form y = mx + c , where m is the slope and c is the y intercept<\/p>\n<p>Non linear function: The graph of a linear function shows a constant rate of change, A non linear function does not have a constant rate of change, So its graph is a not a line.<\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use an Example and Non-Example Chart to list examples and non-examples of a concept. Here is an Example and Non-Example Chart for functions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 2\" width=\"421\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-2.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-2-300x249.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 3\" width=\"237\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-3.png 237w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-3-225x300.png 225w\" sizes=\"(max-width: 237px) 100vw, 237px\" \/><br \/>\n1. linear functions<br \/>\n2. nonlinear functions<br \/>\n3. linear functions with positive slope<br \/>\n4. linear functions with negative slope<\/p>\n<p>Answer: 1. linear functions <img loading=\"lazy\" class=\"alignnone size-full wp-image-55079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-59.png\" alt=\"\" width=\"454\" height=\"396\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-59.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-59-300x262.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 4\" width=\"594\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-4.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-4-300x39.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p><strong>7.1 Relations and Functions (pp. 275\u2013280)<\/strong><br \/>\nLearning Target: Understand the concept of a function.<\/p>\n<p>List the ordered pairs shown in the mapping diagram. Then determine whether the relation is a function.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 5\" width=\"156\" height=\"137\" \/><br \/>\nAnswer: The ordered pairs are ( 1 , -4 ) , ( 3 , 6 ) , ( 5 , 0 ) , ( 7 , 6 ) , ( 7 , 8 ) and The relation is not a function .<\/p>\n<p>Explanation:<br \/>\nAs shown , The ordered pairs are ( 1 , -4 ) , ( 3 , 6 ) , ( 5 , 0 ) , ( 7 , 6 ) , ( 7 , 8 ) .<br \/>\nThe input 7 has more than one output,<br \/>\nSo, The relation is not a function .<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 6\" width=\"159\" height=\"132\" \/><br \/>\nAnswer: ordered pairs are ( 0 , 0 ) , ( 1 , 10 ) , ( 2 , 5 ) , ( 3 , 15 ) and The relation is a function .<\/p>\n<p>Explanation:<br \/>\nAs shown , The ordered pairs are ( 0 , 0 ) , ( 1 , 10 ) , ( 2 , 5 ) , ( 3 , 15 ).<br \/>\nEach input has exactly one output ,<br \/>\nSo, The relation is a function .<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 7\" width=\"163\" height=\"144\" \/><br \/>\nAnswer: The ordered pairs are ( -1 , 0 ) , ( -1 , 1 ) , ( 0 , 1 ) , ( 1 , 2 ), ( 3 ,3 ) and The relation is not a function<\/p>\n<p>Explanation:<br \/>\nAs shown , The ordered pairs are ( -1 , 0 ) , ( -1 , 1 ) , ( 0 , 1 ) , ( 1 , 2 ), ( 3 ,3 ) .<br \/>\nThe input -1 has more than one output ,<br \/>\nSo, The relation is not a function .<\/p>\n<p>Question 4.<br \/>\nFor ordered pairs that represent relations, which coordinate represents the input? the output?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 8\" width=\"164\" height=\"169\" \/><br \/>\nAnswer: x coordinate is the input and y coordinate is the output<\/p>\n<p>Explanation:<br \/>\nOrdered pairs from the given graph are ( 2 , 7 ) , ( 3 , 7 ) , ( 4 , 5 ) , ( 5 , 5 ) , ( 6 , 3 ) .<br \/>\nSo , x coordinate is the input and y coordinate is the output<\/p>\n<p>Question 5.<br \/>\nDraw a mapping diagram that represents the relation shown in the graph. Then determine whether the relation is a function. Explain.<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nThe mapping diagram is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-60.png\" alt=\"\" width=\"181\" height=\"232\" \/><br \/>\neach input has more than one output<br \/>\nSo, relation is not a function.<\/p>\n<p>Question 6.<br \/>\nThe mapping diagram represents the lengths (in centimeters) of a rubber band when different amounts of force (in Newtons) are applied.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 9\" width=\"159\" height=\"169\" \/><br \/>\na. Is the length of a rubber band a function of the force applied to the rubber band?<br \/>\nb. Describe the relationship between the length of a rubber band and the force applied to the rubber band.<br \/>\nAnswer:\u00a0 a. Yes<br \/>\nb. For every increase in 0.7 in input there is an increment of 2 in output.<\/p>\n<p>Explanation:<br \/>\na. The ordered pairs are \u00a0( 0 , 5 ) , ( 0.7 , 7 ) , ( 1.4 , 9 ) , ( 2.1 , 11 )<br \/>\nEach input has exactly one output<br \/>\nSo, the length of a rubber band a function of the force applied to the rubber band.<\/p>\n<p>b. For every increase in 0.7 in input there is an increment of 2 in output.<\/p>\n<p><strong>7.2 Representations of Functions (pp. 281\u2013288)<\/strong><br \/>\nLearning Target: Represent functions in a variety of ways.<\/p>\n<p><strong>Write a function rule for the statement.<\/strong><br \/>\nQuestion 7.<br \/>\nThe output is two less than the input.<br \/>\nAnswer: y = x &#8211; 2<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is two less than the input, will be<br \/>\ny = x &#8211; 2<\/p>\n<p>Question 8.<br \/>\nThe output is two more than one-fourth of the input.<br \/>\nAnswer: y = \\(\\frac{x}{4}\\) + 2<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is two more than one-fourth of the input, will be<br \/>\ny = \\(\\frac{x}{4}\\) + 2<\/p>\n<p><strong>Find the value of y for the given value of x.<\/strong><br \/>\nQuestion 9.<br \/>\ny = 2x &#8211; 3; x = &#8211; 4<br \/>\nAnswer: y = -8<\/p>\n<p>Explanation:<br \/>\nGiven, y = 2x<br \/>\nsubstitute x = -4 , we get<br \/>\ny = 2(-4)<br \/>\ny = -8.<\/p>\n<p>Question 10.<br \/>\ny = 2 &#8211; 9x ; x = \\(\\frac{2}{3}\\)<br \/>\nAnswer: y = &#8211; 3.4<\/p>\n<p>Explanation:<br \/>\nGiven , y = 2 &#8211; 9x<br \/>\nsubstitute x = \\(\\frac{2}{3}\\) , we get<br \/>\ny = 2 &#8211; 9 (0.6)<br \/>\ny = 2 &#8211; 5.4<br \/>\ny = &#8211; 3.4<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{x}{3}\\) + 5; x = 6<br \/>\nAnswer: y = 7.<\/p>\n<p>Explanation:<br \/>\nGiven, y = \\(\\frac{x}{3}\\) + 5<br \/>\nsubstitute x = 6 , we get<br \/>\ny = \\(\\frac{6}{3}\\) + 5<br \/>\ny = 2 + 5<br \/>\ny = 7.<\/p>\n<p><strong>Graph the function.<\/strong><br \/>\nQuestion 12.<br \/>\ny = x + 3<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-61.png\" alt=\"\" width=\"479\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-61.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-61-300x260.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = x + 3\u00a0 , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 0 + 3 = 3 . co-ordinates are (0 , 4)<br \/>\nif x = 1 , then y = 1 + 3\u00a0 = 4 . co-ordinates are (1 , 5)<br \/>\nif x = 2 , then y = 2 + 3 = 5 , co-ordinates are (2 , 6)<br \/>\nif x = 3 , then y = 3 + 3 = 6 , co-ordinates are (3 , 7)<br \/>\nThe co-ordinates (0 , 3) , (1 , 4) , (2 , 5) , (3 , 6) form a straight line .<\/p>\n<p>Question 13.<br \/>\ny = &#8211; 5x<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41.1.png\" alt=\"\" width=\"588\" height=\"367\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41.1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-41.1-300x187.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; 5x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =- 5(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = &#8211; 5(1) \u00a0= &#8211; 5 . co-ordinates are (1 , &#8211; 5)<br \/>\nif x = 2 , then y = &#8211; 5(2) = -10 , co-ordinates are (2 , -10)<br \/>\nif x = 3 , then y =- 5(3) = -15 , co-ordinates are (3 , -15)<br \/>\nThe co-ordinates (0 , 0) , (1 , -5) , (2 , -10) , (3 , -15) form a straight line .<\/p>\n<p>Question 14.<br \/>\ny = 3 &#8211; 3x<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-62.png\" alt=\"\" width=\"586\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-62.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-62-300x186.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y =3 &#8211; 3x , we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 3 &#8211; 3(0) = 3 . co-ordinates are (0 , 3)<br \/>\nif x = 1 , then y = 3 &#8211; 3(1) \u00a0= 0 . co-ordinates are (1 , 0)<br \/>\nif x = 2 , then y = 3 &#8211; 3(2) = &#8211; 3 , co-ordinates are (2 , &#8211; 3)<br \/>\nif x = 3 , then y =3 &#8211; 3(3) = &#8211; 6 , co-ordinates are (3 , &#8211; 6)<br \/>\nThe co-ordinates (0 , 3) , (1 , 0) , (2 , &#8211; 3) , (3 , &#8211; 6) form a straight line .<\/p>\n<p>Question 15.<br \/>\nAn online music store sells songs for $0.90 each.<br \/>\na. Write a function that you can use to find the cost of buying songs.<br \/>\nb. What is the cost of buying 5 songs?<br \/>\nAnswer: a. C = 0.90s<br \/>\nb. $4.5<\/p>\n<p>Explanation:<br \/>\na. The total cost is equal to the cost of each song times the number of songs, if each song is $0.90,<br \/>\nThen the total cost C of s songs is C = 0.90s.<\/p>\n<p>b. Substituting s= 5 in C = 0.90s we get,<br \/>\nC = 0.90(5) = 4.5.<br \/>\nSo, cost of 5 songs is $4.5.<\/p>\n<p><strong>7.3 Linear Functions (pp. 289\u2013294)<\/strong><br \/>\nLearning Target: Use functions to model linear relationships.<\/p>\n<p><strong>Use the graph or table to write a linear function that relates y to x.<\/strong><br \/>\nQuestion 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 16\" width=\"195\" height=\"122\" \/><br \/>\nAnswer: The linear function is y = <span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\\(\\frac{1}{3}\\)<\/span><\/span><\/span><\/span><\/span><\/span>x + 3.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (3 , 4) , (0 , 3 ) , (-3 , 2) , ( -6, 1 )<br \/>\nFirst find the slope m of the line containing the two given points (0 ,3) and (-3, 2)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (2 \u2013 3) \/ (-3 \u2013 0)<br \/>\nm = -1 \/ -3 .<br \/>\nm = 1\/3 .<br \/>\nBecause the line crosses the y axis at ( 0, 3 ) , The y intercept is 3.<br \/>\nSo , the linear function is y = <span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\\(\\frac{1}{3}\\)<\/span><\/span><\/span><\/span><\/span><\/span>x + 3.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 17\" width=\"192\" height=\"77\" \/><br \/>\nAnswer: The linear function is y =\u00a0<span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\u2212(0)<\/span><\/span><\/span><\/span><\/span><\/span>x -7.<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-2 , -7) , (0 , -7 ) , (2 , -7) , ( 4 , -7 )<br \/>\nFirst find the slope m of the line containing the two given points (0 ,-7) and (2, -7)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (-7 \u2013 (-7)) \/ (2 \u2013 0)<br \/>\nm = 0 .<br \/>\nBecause the line crosses the y axis at ( 0, -7 ) , The y intercept is -7.<br \/>\nSo , the linear function is y =\u00a0<span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\u2212(0)<\/span><\/span><\/span><\/span><\/span><\/span>x -7.<\/p>\n<p>Question 18.<br \/>\nThe table shows the age x (in weeks) of a puppy and its weight y (in pounds).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 18\" width=\"533\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-18.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-18-300x108.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\na. Write and graph a linear function that relates y to x.<br \/>\nb. Interpret the slope and the y-intercept.<br \/>\nc. After how many weeks will the puppy weigh 33 pounds?<br \/>\nAnswer: a. y = \\(\\frac{3}{2}\\)x + 3<br \/>\nb. 3 pounds<br \/>\nc. Age is 20 weeks<\/p>\n<p>Explanation: <img loading=\"lazy\" class=\"alignnone size-full wp-image-55170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-63.png\" alt=\"\" width=\"434\" height=\"382\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-63.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-63-300x264.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\na. In order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (6 , 12) , (8 , 15 ) , (10 , 18) , ( 12 , 21 )<br \/>\nFirst find the slope m of the line containing the two given points ((6 ,12) and (8 , 15)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (15 \u2013 12) \/ (8 \u2013 6)<br \/>\nm = 3\/2 .<br \/>\nsubstitute the slope in the (6 ,12) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 12 = 3\/2 ( x \u2013 6)<br \/>\n2(y \u2013 12) = 3(x \u2013 6)<br \/>\n2y &#8211; 24 = 3x \u2013 18<br \/>\n2y = 3x \u2013 18 + 24<br \/>\n2y\u00a0 = 3x + 6<br \/>\nSo ,\u00a0 2y\u00a0 = 3x + 6 or y = \\(\\frac{3}{2}\\)x + 3 is linear function.<\/p>\n<p>b. The slope measures the rate of change of weight due to change in weeks, Here the slope of 3\/2 means that as one week passes, weight of the puppy increases by 3\/2 pounds.<br \/>\ny intercept measures the weight of the puppy, when it was born which is 3 pounds in this case measured by c.<\/p>\n<p>c. put y = 33,<br \/>\n33 = \\(\\frac3}{2}\\)x + 3<br \/>\n30 = \\(\\frac{3}{2}\\)x<br \/>\n30 \u00d7 2 = 3x<br \/>\nx = 60\/3<br \/>\nx = 20.<br \/>\nSo, Age is 20 weeks.<\/p>\n<p><strong>7.4 Comparing Linear and Nonlinear Functions (pp. 295\u2013300)<\/strong><br \/>\nLearning Target: Understand differences between linear and nonlinear functions.<\/p>\n<p><strong>Does the table represent a linear or nonlinear function? Explain.<\/strong><br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 19\" width=\"183\" height=\"72\" \/><br \/>\nAnswer: y = 3x \u2013 8 is linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (3 , 1 ) , (6 , 10) , (9 , 19) , (12 , 28)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (3 , 1 ) and (6 , 10)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (10 \u2013 1) \/ (6\u2013 3)<br \/>\nm = 9\/3<br \/>\nm = 3<br \/>\nsubstitute the slope in the (3 , 1) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 1 = 3 ( x \u2013 3)<br \/>\ny \u2013 1 = 3x \u2013 9<br \/>\ny = 3x \u2013 9 + 1<br \/>\ny = 3x \u2013 8<br \/>\nSo ,\u00a0 y = 3x \u2013 8 is linear function.<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 20\" width=\"198\" height=\"67\" \/><br \/>\nAnswer: y = -x + 4 is linear function.<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are (1 , 3 ) , (3 , 1) , (5 , 1) , (7 , 3)<br \/>\nPlot the points in the table , Draw a line through the points<br \/>\nFirst find the slope m of the line containing the two given points (1 , 3 ) and (3 , 1)<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (1 \u2013 3) \/ (3\u2013 1)<br \/>\nm = -2\/2<br \/>\nm = -1<br \/>\nsubstitute the slope in the (1 , 3) to get point slope to form a line.<br \/>\ny-y<sub>1<\/sub>\u00a0= m\u00a0(x-x<sub>1<\/sub>)<br \/>\ny \u2013 3 = -1 ( x \u2013 1)<br \/>\ny \u2013 3 = -x + 1<br \/>\ny = -x + 1 + 3<br \/>\ny = -x + 4<br \/>\nSo ,\u00a0 y = -x + 4 is linear function.<\/p>\n<p>Question 21.<br \/>\nDoes the graph represent a linear or nonlinear function? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 21\" width=\"176\" height=\"171\" \/><br \/>\nAnswer: The graph represent a non linear function.<\/p>\n<p>Explanation:<br \/>\nAs shown in the graph linear function represents a\u00a0 straight line to which not happened here,<br \/>\nSo , the graph is non linear function<\/p>\n<p>Question 22.<br \/>\nDoes the equation y = 2.3x represent a linear or nonlinear function? Explain.<br \/>\nAnswer: y = 2.3x is a linear function.<\/p>\n<p>Explanation:<br \/>\nGiven , y = 2.3x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y = 2.3(0) = 0 . co-ordinates are (0 , 0)<br \/>\nif x = 1 , then y = 2.3(1) = 2.3 . co-ordinates are (1 , 2.3)<br \/>\nif x = 2 , then y = 2.3(2) = 4.6 , co-ordinates are (2 , 4.6)<br \/>\nThe co-ordinates (0 , 0) , (1 , 2.3) , (2 , 4.6) form a straight line .<br \/>\nEach x input has only one y output so it is a function .<br \/>\nAnd it\u00a0 forms a straight line when graphed .<br \/>\nSo, y = 2.3x is a linear function.<\/p>\n<p><strong>7.5 Analyzing and Sketching Graphs (pp. 301\u2013306)<\/strong><br \/>\nLearning Target: Use graphs of functions to describe relationships between quantities.<\/p>\n<p>Question 23.<br \/>\nDescribe the relationship between the two quantities in the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-23.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 23\" width=\"182\" height=\"180\" \/><br \/>\nAnswer: At certain point of time, line segment is increased with respect to time and maintained a constant change and again dropped gradually with the increase in time.<\/p>\n<p>Explanation:<br \/>\nThe relationship between the graph is population and time ,<br \/>\nAt certain point of time, line segment is increased with respect to time and maintained a constant change and again dropped gradually with the increase in time.<br \/>\nSo, the city population is not constant at all the time.<\/p>\n<p><strong>Sketch a graph that represents the situation.<\/strong><br \/>\nQuestion 24.<br \/>\nYou climb a climbing wall. You climb halfway up the wall at a constant rate, then stop and take a break. You then climb to the top of the wall at a greater constant rate.<br \/>\nAnswer: The graph is\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-55177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-64.png\" alt=\"\" width=\"333\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-64.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-64-300x225.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Explanation:<br \/>\nYou start climbing a wall at a constant rate so the first portion of the graph needs to be linear with a positive slope, you then take a break which means your height is constant so the second part of the graph needs to be a horizontal line, you then start climbing again at a constant rate, so the last part of the graph needs to be linear with a positive slope.<\/p>\n<p>Question 25.<br \/>\nThe price of a stock increases at a constant rate for several months before the stock market crashes. The price then quickly decreases at a constant rate.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-65.png\" alt=\"\" width=\"198\" height=\"174\" \/><\/p>\n<p>Explanation:<br \/>\nThe stock price is increasing at a constant rate so the first part of the graph needs to be linear with positive slope, Then price begins to drop quickly so the second part of the graph needs to be linear with a steep negative slope.<\/p>\n<p>Question 26.<br \/>\nThe graph shows the sales of two companies during a particular year.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-7-Functions-cr-26.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 7 Functions cr 26\" width=\"172\" height=\"150\" \/><br \/>\na. Describe the sales of each company.<br \/>\nb. Which company has greater total sales for the year?<br \/>\nc. Give a possible explanation for the change in each company&#8217;s sales throughout the year.<br \/>\nAnswer: All The explanation is given below<\/p>\n<p>a. Company A &#8211; The sales of the company is increasing at a constant rate so the first part of the graph needs to be linear with positive slope, and decreasing with a slight negative steep and again increasing at a constant rate increasing the sales of the company<\/p>\n<p>Company B &#8211; The sales of the company is increasing at a constant rate so the first part of the graph needs to be increase in curve with a slight decrease in the graph leading to decrease in sales and vise versa.<\/p>\n<p>b. Company A has the greater total sales for the year compared to Company B, with maintaining the sales up to the mark without losses.<\/p>\n<p>c. The change in each company&#8217;s sales throughout the year,\u00a0 Company A &#8211; The sales of the company is increasing at a constant rate so the first part of the graph needs to be linear with positive slope,<br \/>\nCompany B &#8211; The sales of the company is increasing at a constant rate so the first part of the graph needs to be increase in curve with a slight decrease in the graph leading to decrease in sales<\/p>\n<h3><a id=\"Functions _Practice _Test\"><\/a>Functions Practice Test<\/h3>\n<p>Question 1.<br \/>\nList the ordered pairs shown in the mapping diagram. Then determine whether the relation is a function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 1\" width=\"165\" height=\"119\" \/><br \/>\nAnswer: The relation is a function<\/p>\n<p>Explanation:<br \/>\nAs shown , Ordered pairs are the combinations of input and output<br \/>\nSo , Ordered pairs are ( 2 , 9 ) , ( 4 , 9 ) , ( 6 , 10 ) , ( 8 , 11 ) .<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 2.<br \/>\nDraw a mapping diagram that represents the relation. Then determine whether the relation is a function. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 2\" width=\"158\" height=\"139\" \/><br \/>\nAnswer: The mapping diagram is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-66.png\" alt=\"\" width=\"166\" height=\"206\" \/><\/p>\n<p>Explanation:<br \/>\nOrdered pairs from the given graph are ( -3 , 5 ) , ( -1 , 1 ) , ( -1 , 3 ) , ( 1 , 2 ) , ( 3 , 4 ) .<br \/>\nEach input has exactly one output ,<br \/>\nSo , The relation is a function .<\/p>\n<p>Question 3.<br \/>\nWrite a function rule for \u201cThe output is twice the input.\u201d<br \/>\nAnswer: y = 2x<\/p>\n<p>Explanation:<br \/>\nLet us say x is input and y is output , then<br \/>\nThe output is twice the input. will be<br \/>\ny = 2x<\/p>\n<p>Question 4.<br \/>\nGraph the function y = 1 &#8211; 3x.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-67.png\" alt=\"\" width=\"623\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-67.png 623w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-67-300x195.png 300w\" sizes=\"(max-width: 623px) 100vw, 623px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven , y = 1 &#8211; 3x \u00a0, we know y = mx + c , where m = slope , c = constant<br \/>\nTo obtain the graph , we should have ordered pairs ,<br \/>\nSo , if x = 0 , then y =1 &#8211; 3(0) = 1 . co-ordinates are (0 , 1)<br \/>\nif x = 1 , then y = 1 &#8211; 3(1) \u00a0= -2 . co-ordinates are (1 , -2)<br \/>\nif x = 2 , then y = 1 &#8211; 3(2) = -5 , co-ordinates are (2 , -5)<br \/>\nif x = 3 , then y =1 &#8211; 3(3) = -8 , co-ordinates are (3 , -8)<br \/>\nThe co-ordinates (0 , 1) , (1 , -2) , (2 , -5) , (3 , -8) form a straight line .<\/p>\n<p>Question 5.<br \/>\nUse the graph to write a linear function that relates y to x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 5\" width=\"166\" height=\"140\" \/><br \/>\nAnswer: The linear function is y = 0.5x &#8211; 1<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (-4 , -3) , (-2 , -2 ) , (0 , -1) , ( 2 , 0 )<br \/>\nFirst find the slope m of the line containing the two given points (0 , -1) and ( 2 , 0 )<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (0 \u2013 (-1)) \/ (2 \u2013 0)<br \/>\nm = 1 \/ 2 .<br \/>\nm = 0.5 .<br \/>\nBecause the line crosses the y axis at ( 0, -1 ) , The y intercept is -1.<br \/>\nSo , the linear function is y = 0.5x &#8211; 1 .<\/p>\n<p>Question 6.<br \/>\nDoes the table represent a linear or nonlinear function? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 6\" width=\"207\" height=\"74\" \/><br \/>\nAnswer: The linear function is y =\u00a0<span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\u22124<\/span><\/span><\/span><\/span><\/span><\/span>x + 8<\/p>\n<p>Explanation:<br \/>\nIn order to write the function we have to write the ordered pairs of the graph ,<br \/>\nOrdered pairs are\u00a0 (0 , 8) , (2 , 0 ) , (4 , -8) , ( 6 , -16 )<br \/>\nFirst find the slope m of the line containing the two given points (0 , 8) and (2 , 0 )<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (0 \u2013 8) \/ (2 \u2013 0)<br \/>\nm = -4<br \/>\nBecause the line crosses the y axis at ( 0, 8 ) , The y intercept is 8.<br \/>\nSo , the linear function is y =\u00a0<span id=\"MathJax-Element-59-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-390\" class=\"math\"><span id=\"MathJax-Span-391\" class=\"mrow\"><span id=\"MathJax-Span-392\" class=\"mfrac\"><span id=\"MathJax-Span-393\" class=\"mrow\"><span id=\"MathJax-Span-394\" class=\"mo\">\u22124<\/span><\/span><\/span><\/span><\/span><\/span>x + 8.<\/p>\n<p>Question 7.<br \/>\nThe table shows the number of y meters a water-skier travels in x minutes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 7\" width=\"289\" height=\"82\" \/><br \/>\na. Write a function that relates y to x.<br \/>\nb. Graph the linear function.<br \/>\nc. At this rate, how many kilometers will the water-skier travel in 12 minutes?<br \/>\nd. Another water-skier travels at the same rate but starts a minute after the first water-skier. Will this water-skier catch up to the first water-skier? Explain.<br \/>\nAnswer: All the answers are given below<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are\u00a0 (1 , 600) , (2 , 1200 ) , (3 , 1800) , ( 4 , 2400 ) , (5 , 3000)<br \/>\nFirst find the slope m of the line containing the two given points(1 , 600) and (2 , 1200 )<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (1200 \u2013 600) \/ (2 \u2013 1)<br \/>\nm = 600<br \/>\nSo, the line is of the form y = 600x + c<br \/>\nput x= 3 and y = 1800 in the above equation we get,<br \/>\n1800 = 600(3) + c<br \/>\nc = 1800 &#8211; 1800<br \/>\nc = 0.<br \/>\nSo, The line is y = 600x.<\/p>\n<p>b. The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-69.png\" alt=\"\" width=\"732\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-69.png 732w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-69-300x180.png 300w\" sizes=\"(max-width: 732px) 100vw, 732px\" \/><\/p>\n<p>c. put x = 12 in y = 600x<br \/>\ny = 600(12)<br \/>\ny = 7200<br \/>\n7200 meters, i.e., 7.2km<\/p>\n<p>d. Another water skier travels at the same rate but starts a minute after the first water skier, Since both are travelling at the same rate , the water skier who was late will always be behind the first water skier.<\/p>\n<p>Question 8.<br \/>\nThe graph shows the prices of two stocks during one day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-pt-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions pt 8\" width=\"183\" height=\"143\" \/><br \/>\na. Describe the changes in the price of each stock.<br \/>\nb. Which stock has a greater price at the end of the day?<br \/>\nc. Give a possible explanation for the change in the price of Stock B throughout the day.<br \/>\nAnswer: Detailed Explanation is given below.<\/p>\n<p>Explanation:<br \/>\na. The changes in the price of each stock is Stock A has the constant increase in stock for a particular time and maintains a constant price forming a straight line in the graph, and again decreasing with a negative slope and vise versa, while Stock B is having steep negative slope that is decreasing in the prices with the time and having a constant horizontal line. and having a positive increase in the slope and same repeats again.<\/p>\n<p>b. stock B has a greater price at the end of the day, having a positive increase in the slope<\/p>\n<p>c. The change in the price of Stock B throughout the day, is having steep negative slope that is decreasing in the prices with the time and having a constant horizontal line. and having a positive increase in the slope and same repeats again, compared to stock A .<\/p>\n<p>Question 9.<br \/>\nYou are competing in a footrace. You begin the race by increasing your speed at a constant rate. You then run at a constant speed until you get a cramp and have to stop. You wait until your cramp goes away before you start increasing your speed again at a constant rate. Sketch a graph that represents the situation.<br \/>\nAnswer: The graph is <img loading=\"lazy\" class=\"alignnone size-full wp-image-55191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-68.png\" alt=\"\" width=\"338\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-68.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-68-300x178.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Explanation:<br \/>\nYou begin the race by increasing your speed at a constant rate so the first portion of the graph needs to be linear with a positive slope , you then run at a constant speed so the next portion of the graph needs to be horizontal line , you then stop and take a break , so your speed is zero, which means the next portion of the line needs to be<br \/>\nhorizontal line on the x axis , you then increase your speed again at a constant rate sop that the last portion of the graph needs to be linear with a positive slope<\/p>\n<h3><a id=\"Functions _Cumulative _Practice\"><\/a>Functions Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 1\" width=\"298\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-1.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-1-262x300.png 262w\" sizes=\"(max-width: 298px) 100vw, 298px\" \/><br \/>\nQuestion 1.<br \/>\nWhat is the slope of the line?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 2\" width=\"246\" height=\"299\" \/><br \/>\nAnswer: Not in the options but the answer is m = -4\/3<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are\u00a0 (-4 , 5) , (1 , -3 ),<br \/>\nFirst find the slope m of the line containing the two given points<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (-3 \u2013 5) \/ (2 \u2013 (-4))<br \/>\nm = -8\/6<br \/>\nm = -4\/3.<\/p>\n<p>Question 2.<br \/>\nWhich value of a makes the equation 24 = \\(\\frac{a}{3}\\) &#8211; 9 true?<br \/>\nF. 5<br \/>\nG. 11<br \/>\nH. 45<br \/>\nI. 99<br \/>\nAnswer: I. 99<\/p>\n<p>Explanation:<br \/>\nSubstitute a = 99 , in the given equation we get,<br \/>\n24 = \\(\\frac{a}{3}\\) &#8211; 9<br \/>\n24 = \\(\\frac{99}{3}\\) &#8211; 9<br \/>\n24 = 33 &#8211; 9<br \/>\n24 = 24.<br \/>\nSo, last option is the correct answer.<\/p>\n<p>Question 3.<br \/>\nA mapping diagram is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 3\" width=\"273\" height=\"146\" \/><br \/>\nWhat number belongs in the box so that the equation describes the function represented by the mapping diagram?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 5\" width=\"123\" height=\"50\" \/><br \/>\nAnswer: m = 7 , y = 7x + 5<\/p>\n<p>Explanation:<br \/>\nOrdered pairs are\u00a0 (4 , 33) , (7 , 54 ), (10 , 75) , (13 , 96 ),<br \/>\nFirst find the slope m of the line containing the two given points (4 , 33) and (7 , 54 )<br \/>\nm = (y<sub>2<\/sub>-y<sub>1<\/sub>) \/ (x<sub>2<\/sub>-x<sub>1<\/sub>)<br \/>\nm= (54 \u2013 33) \/ (7 &#8211; 4)<br \/>\nm = 21\/3<br \/>\nm = 7.<br \/>\nSo, y = 7x + 5<\/p>\n<p>Question 4.<br \/>\nWhat is the solution of the system of linear equations?<br \/>\n3x + 2y = 5<br \/>\nx = y + 5<br \/>\nA. (3, &#8211; 2)<br \/>\nB. (- 2, 3)<br \/>\nC. (- 1, 4)<br \/>\nD. (1, &#8211; 4)<br \/>\nAnswer: A. (3, &#8211; 2)<\/p>\n<p>Explanation:<br \/>\nGiven 3x + 2y = 5<br \/>\nThen substitute , x = y + 5 in the above equation<br \/>\n3( y + 5) + 2y = 5<br \/>\n3y + 15 + 2y = 5<br \/>\n5y + 15 = 5<br \/>\n5( y + 3) = 5<br \/>\ny + 3 = 1<br \/>\ny = 1 &#8211; 3<br \/>\ny = -2,<br \/>\nsubstitute y = -2 in x = y + 5 then<br \/>\nx = 3<br \/>\nSo, (3 , -2)<\/p>\n<p>Question 5.<br \/>\nThe director of a research lab wants to present data to donors. The data show how the lab uses a large amount of donated money for research and only a small amount of money for other expenses. Which type of display best represents these data?<br \/>\nF. box-and-whisker plot<br \/>\nG. circle graph<br \/>\nH. line graph<br \/>\nI. scatter plot<br \/>\nAnswer: I. scatter plot<\/p>\n<p>Explanation:<br \/>\nScatter plot is the best graph for this type of data where vertical axis will show the amount of money and Horizontal axis will show research and other expenses.<\/p>\n<p>Question 6.<br \/>\nWhich graph shows a nonlinear function?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 6\" width=\"479\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-6.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-6-300x195.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nAnswer: option B<\/p>\n<p>Explanation:<br \/>\nAs all the other options are representing the linear function that is forming a straight line\u00a0 expect for option B , it is representing a non linear equation.<\/p>\n<p>Question 7.<br \/>\nWhich equation of a line passes through the point (\u20142, 3) and has a slope of \\(\\frac{3}{4}\\)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 7\" width=\"161\" height=\"188\" \/><br \/>\nAnswer:\u00a0 F. y &#8211; 3 = \\(\\frac{3}{4}\\)(x + 2)<\/p>\n<p>Explanation:<br \/>\nGiven, y &#8211; 3 = \\(\\frac{3}{4}\\)(x + 2)<br \/>\nit is in the form of y = mx + c<br \/>\nso, slope m = \\(\\frac{3}{4}\\)<br \/>\nSubstitute the given points in this equation that is x = -2 and y = 3<br \/>\n3 &#8211; 3 = \\(\\frac{3}{4}\\)(-2 + 2)<br \/>\n0 = 0.<br \/>\nSo, F is the correct option.<\/p>\n<p>Question 8.<br \/>\nThe tables show the sales (in millions of dollars) for two companies over a five-year period.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 8\" width=\"324\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-8.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-8-300x114.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nPart A Does the first table show a linear function? Explain your reasoning.<br \/>\nPart B Does the second table show a linear function? Explain your reasoning.<br \/>\nAnswer: Part A, the first table shows a linear function,<br \/>\nPart B the second table shows a linear function.<\/p>\n<p>Explanation:<br \/>\nPart A &#8211; ordered pairs are (1 , 2) , (2 , 4) , (3 , 6) , (4 , 8) , (5 , 10)<br \/>\nEach input has exactly one output and forms a straight line when graphed<br \/>\nSo, it is a linear function.<\/p>\n<p>Part B &#8211; ordered pairs are (1 , 1) , (2 , 1) , (3 , 2) , (4 , 3) , (5 , 5)<br \/>\nEach input has exactly one output and does not form a straight line when graphed<br \/>\nSo, it is a linear function.<\/p>\n<p>Question 9.<br \/>\nThe equations y = &#8211; x + 4 and y = \\(\\frac{1}{2}\\)x &#8211; 8 form a system of linear equations. The table shows the values of y for given values of x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 9\" width=\"422\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-9.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-9-300x77.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><br \/>\nWhat can you conclude from the table?<br \/>\nA. The system has one solution, when x = 0.<br \/>\nB. The system has one solution, when x = 4.<br \/>\nC. The system has one solution, when x = 8.<br \/>\nD. The system has no solution.<br \/>\nAnswer: C. The system has one solution, when x = 8.<\/p>\n<p>Explanation:<br \/>\nGiven , y = &#8211; x + 4 and y = \\(\\frac{1}{2}\\)x &#8211; 8<br \/>\nfor x = 8 we have<br \/>\ny = -8 + 4 = -4<br \/>\ny = 0.5(8) &#8211; 8 = 4 &#8211; 8 = -4<br \/>\nBoth the equations have one solution for x = 8<br \/>\nSo, The system has one solution, when x = 8.<\/p>\n<p>Question 10.<br \/>\nThe vertices of a triangle are A (- 1, 3), B (1, 2), and C (- 1, &#8211; 1). Dilate the triangle using a scale factor of 2. What is the y-coordinate of the image of B?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-7-Functions-cp-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 7 Functions cp 10\" width=\"77\" height=\"61\" \/><br \/>\nAnswer: The New right angle triangle is larger than the original one So , its a increase .<\/p>\n<p>Explanation:<br \/>\nGiven , (- 1, 3),\u00a0 ( 1, 2 ),\u00a0 (- 1, -1) these pairs form a right angle triangle<br \/>\nK = 2 , For the dilation figure multiply the 3 with the given ordered pairs , then<br \/>\n(- 1, 3) \u00d7 2 = ( -2 , 6)<br \/>\n( 1, 2) \u00d7 2 = ( 2 , 4)<br \/>\n(- 1, -1) \u00d7 2 = (-2 , -2)<br \/>\nFrom these new ordered pairs we form a new\u00a0 right angle triangle<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-55252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-70.png\" alt=\"\" width=\"563\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-70.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-Functions-70-300x216.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><br \/>\nThe New right angle triangle is larger than the original one So, it&#8217;s an increase.<\/p>\n<h3>Conclusion<\/h3>\n<p>Enhance your problem-solving skills and overall math proficiency using the Big Ideas Math Grade 8 Chapter 7 Functions. Give your best in exams by solving the Problems Over here aligned as per the Latest BIM Textbooks. In case of any suggestions do leave us your queries via the comment box so that we can get back to you.<\/p>\n<p>Must Try:<\/p>\n<p><a href=\"https:\/\/paisaalgo.com\/cholafin-pivots-calculator\/\">CHOLAFIN Pivot Calculator<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Grade 8 Chapter 7 Functions is given by subject experts adhering to the latest syllabus guidelines. Become Proficient in the Concepts of Big Ideas Math Grade 8 Functions by consistently practicing from our BIM Book 8th Grade Ch 7 Functions Answer Key. To make it easy for you to understand the concepts &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 7 Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-7\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 7 Functions\">Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":89300,"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\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-7-1.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31757"}],"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\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=31757"}],"version-history":[{"count":2,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31757\/revisions"}],"predecessor-version":[{"id":92885,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/31757\/revisions\/92885"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89300"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=31757"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=31757"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=31757"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}