{"id":32964,"date":"2022-04-07T10:32:46","date_gmt":"2022-04-07T05:02:46","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=32964"},"modified":"2022-04-07T11:40:07","modified_gmt":"2022-04-07T06:10:07","slug":"big-ideas-math-answers-grade-8-chapter-4","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-4\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations"},"content":{"rendered":"<p>Are you searching everywhere regarding the Big Ideas Math 8th Grade Answer Key Chapter 4 Graphing and Writing Linear Equations? If so, halt your search as this is the one-stop destination for all your needs. Practice using the Graphing and Writing Linear Equations <strong>Big Ideas Math Grade 8 Answers<\/strong> and understand the concepts easily. Begin your preparation right away and seek the homework help needed right after class in a matter of seconds.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 4 Graphing and Writing Linear Equations<\/h2>\n<p>Make the most out of the handy resources available for Big Ideas Math Ch 4 Graphing and Writing Linear Equations and stand out from the rest of the crowd. BIM Book 8th Grade Chapter 4 Solutions include questions belonging to Lessons 4.1 to 4.7, Cumulative Practice, Assessment Tests, Review Tests, etc. Big Ideas Math 8th Grade Chapter 4 Solution Key is given by subject experts after extensive research. Access the quick links over here during your preparation and get the assistance needed at the comfort of your home.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_STEAM_Video\/Performance_Task\">Graphing and Writing Linear Equations STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_Getting_Ready_for_Chapter_4\">Graphing and Writing Linear Equations Getting Ready for Chapter 4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Graphing Linear Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.1_Graphing_Linear_Equations\">Lesson 4.1 Graphing Linear Equations<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Equations_Homework_&amp;_Practice_4.1\">Graphing Linear Equations Homework &amp; Practice 4.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Slope of a Line<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.2_Slope_of_a_Line\">Lesson 4.2 Slope of a Line<\/a><\/li>\n<li><a href=\"#Slope_of_a_Line_Homework_&amp;_Practice_4.2\">Slope of a Line Homework &amp; Practice 4.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Graphing Proportional Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.3_Graphing_Proportional_Relationships\">Lesson 4.3 Graphing Proportional Relationships<\/a><\/li>\n<li><a href=\"#Graphing_Proportional_Relationships_Homework_&amp;_Practice_4.3\">Graphing Proportional Relationships Homework &amp; Practice 4.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Graphing Linear Equations in Slope-Intercept Form<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.4_Graphing_Linear_Equations_in_Slope_Intercept_Form\">Lesson 4.4 Graphing Linear Equations in Slope-Intercept Form<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Equations_in_Slope_Intercept_Form_Homework_&amp;_Practice_4.4\">Graphing Linear Equations in Slope-Intercept Form Homework &amp; Practice 4.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Graphing Linear Equations in Standard Form<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.5_Graphing_Linear_Equations_in_Standard_Form\">Lesson 4.5 Graphing Linear Equations in Standard Form<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Equations_in_Standard_Form_Homework_&amp;_Practice_4.5\">Graphing Linear Equations in Standard Form Homework &amp; Practice 4.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Writing Equations in Slope-Intercept Form<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.6_Writing_Equations_in_Slope_Intercept_Form\">Lesson 4.6 Writing Equations in Slope-Intercept Form<\/a><\/li>\n<li><a href=\"#Writing_Equations_in_Slope_Intercept_Form_Homework_&amp;_Practice_4.6\">Writing Equations in Slope-Intercept Form Homework &amp; Practice 4.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Writing Equations in Point-Slope Form<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_4.7_Writing_Equations_in_Point_Slope_Form\">Lesson 4.7 Writing Equations in Point-Slope Form<\/a><\/li>\n<li><a href=\"#Writing_Equations_in_Point_Slope_Form_Homework_&amp;_Practice_4.7\">Writing Equations in Point-Slope Form Homework &amp; Practice 4.7<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 4 &#8211; Graphing and Writing Linear Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_Connecting_Concepts\">Graphing and Writing Linear Equations Connecting Concepts<\/a><\/li>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_Chapter_Review\">Graphing and Writing Linear Equations Chapter Review<\/a><\/li>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_Practice_Test\">Graphing and Writing Linear Equations Practice Test<\/a><\/li>\n<li><a href=\"#Graphing_and_Writing_Linear_Equations_Cumulative_Practice\">Graphing and Writing Linear Equations Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_STEAM_Video\/Performance_Task\"><\/a>Graphing and Writing Linear Equations STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>\u201cHurricane<br \/>\nA hurricane is a storm with violent winds. How can you prepare your home for a hurricane?<br \/>\nWatch the STEAM Video \u201cHurricane!\u201d Then answer the following questions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 1\" width=\"204\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-1.png 204w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-1-136x300.png 136w\" sizes=\"(max-width: 204px) 100vw, 204px\" \/><br \/>\n1. Robert says that the closer you are to the eye of a hurricane, the stronger the winds become. The wind speed on an island is 50 miles per hour when the eye of a hurricane is 140 miles away.<br \/>\na. Describe the wind speed on the island when the eye of the hurricane is 100 miles away.<br \/>\nb. Describe the distance of the island from the eye of the hurricane when the wind speed on the island is 25 miles per hour.<br \/>\nc. Sketch a line that could represent the wind speed y (in miles per hour) on the island when the eye of x the hurricane is miles away from the island. Wind speed<br \/>\n2. A storm dissipates as it travels over land. What does this mean?<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Anatomy of a Hurricane<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given information about the atmospheric pressure inside a hurricane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 2\" width=\"540\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-2.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-2-300x184.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nYou will be asked to use a model to find the strength of a hurricane after x hours of monitoring. Why is it helpful to predict how strong the winds of a hurricane will become?<\/p>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_Getting_Ready_for_Chapter_4\"><\/a>Graphing and Writing Linear Equations Getting Ready for Chapter 4<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\n1. Work with a partner.<br \/>\na. Use the equation y = \\(\\frac{1}{2}\\)x + 1 to complete the table. (Choose any two x-values and find the y-values.)<br \/>\nb. Write the two ordered pairs given by the table. These are called solutions of the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 3.1\" width=\"205\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3.1.png 205w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3.1-199x300.png 199w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\nc. PRECISION Plot the two solutions. Draw a line exactly through the points.<br \/>\nd. Find a different point on the line. Check that this point is a solution of the equation y = \\(\\frac{1}{2}\\)x + 1.<br \/>\ne. <strong>LOGIC<\/strong> Do you think it is true that any point on the line is a solution of the equation y = \\(\\frac{1}{2}\\)x + 1? Explain.<br \/>\nf. Choose five additional x-values for the table below. (Choose both positive and negative x-values.) Plot the five corresponding solutions. Does each point lie on the line?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 3\" width=\"397\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-3-300x74.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\ng.<strong> LOGIC<\/strong> Do you think it is true that any solution of the equation y = \\(\\frac{1}{2}\\)x + 1 is a point on the line? Explain.<br \/>\nh. Why do you think y = ax + b is called a linear equation?<\/p>\n<p>Vocabulary<br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nlinear equation<br \/>\nslope<br \/>\ny-intercept<br \/>\nsolution of a linear equation<br \/>\nx-intercept<\/p>\n<h3><a id=\"Lesson_4.1_Graphing_Linear_Equations\"><\/a>Lesson 4.1 Graphing Linear Equations<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Creating Graphs<br \/>\nWork with a partner. It starts snowing at midnight in Town A and Town B. The snow falls at a rate of 1.5 inche sper hour.<br \/>\na. In Town A, there is no snow on the ground at midnight. How deep is the snow at each hour between midnight and 6 A.M.? Make a graph that represents this situation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 1\" width=\"272\" height=\"261\" \/><br \/>\nb. Repeat part(a) for TownB, which has 4 inches of snow on the ground at midnight.<br \/>\nc. The equations below represent the depth y(in inches) of snow x hours after midnight in Town C and Town D. Graph each equation.<br \/>\nTown C y = 2x + 3<br \/>\nTown D y = 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 2\" width=\"430\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-2.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-2-300x137.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><br \/>\nd. Use your graphs to compare the snowfall in each town.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 3\" width=\"187\" height=\"99\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Graph the linear equation<\/strong>.<br \/>\nQuestion 1.<br \/>\ny = 3x<br \/>\nAnswer:<br \/>\nMake to table of values<br \/>\nReplace x with a number and find the value of y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1-300x155.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_1\" width=\"300\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1-300x155.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.png 457w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlot the values of x and y obtained above, on the graph<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.1-300x197.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_1.1\" width=\"300\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.1-300x197.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.1.png 585w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Draw the line through the points<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-74798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.2-300x260.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_1.2\" width=\"300\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.2-300x260.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_1.2.png 501w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\ny = &#8211; 2x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.1-300x155.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_2.1\" width=\"300\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.1-300x155.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.1.png 457w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlot the values of x and y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.2-300x171.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_2.2\" width=\"300\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.2-300x171.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.2.png 545w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nNow the line through the points<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.3-300x182.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_2.3\" width=\"300\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.3-300x182.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_2.3.png 583w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.1-300x197.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_3.1\" width=\"300\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.1-300x197.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.1.png 507w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlot the ordered pairs<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.2-300x195.png\" alt=\"Big ideas math answers grade 8 chapter 4 img_3.2\" width=\"300\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.2-300x195.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answers-grade-8-chapter-4-img_3.2.png 717w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 4.<br \/>\ny = 3<br \/>\nAnswer:<br \/>\nThe graph of y = 3 is a horizontal like passing through (0, 3)<br \/>\nDraw a horizontal line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_4-300x250.png\" alt=\"Big ideas math answer key grade 8 chapter 4 img_4\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_4-300x250.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_4.png 591w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\ny = &#8211; 1.5<br \/>\nAnswer:<br \/>\nThe graph of y = -1.5 is a horizontal line passing through (0, -1.5)<br \/>\nDraw a horizontal line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_5-300x195.png\" alt=\"Big ideas math answer key grade 8 chapter 4 img_5\" width=\"300\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_5-300x195.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-ideas-math-answer-key-grade-8-chapter-4-img_5.png 619w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 6.<br \/>\nx = &#8211; 4<br \/>\nAnswer:<br \/>\nThe graph of x = &#8211; 4 is a vertical line passing through (-4, 0)<br \/>\nDraw a vertical line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_6-300x267.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_6\" width=\"300\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_6-300x267.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_6.png 419w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nx = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nThe graph of x = \\(\\frac{1}{2}\\) is a vertical line passing through (\\(\\frac{1}{2}\\), 0)<br \/>\nDraw a vertical line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_7-300x250.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 4 img_7\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_7-300x250.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_7.png 477w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/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>GRAPHING A LINEAR EQUATION<\/strong> Graph the linear equation.<br \/>\nQuestion 8.<br \/>\ny = &#8211; x + 1<br \/>\nAnswer:<br \/>\nMake of a table of values<br \/>\nReplace x with a number and find the value of y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.1-300x199.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 4 img_8.1\" width=\"300\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.1-300x199.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.1.png 513w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nPlot the values of x and y obtained, on the graph,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.2-300x210.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 4 img_8.2\" width=\"300\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.2-300x210.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_8.2.png 461w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 9.<br \/>\ny = 0.8x &#8211; 2<br \/>\nAnswer:<br \/>\nReplace x with a number and find the value of y<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.1-300x204.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 4 img_9.1\" width=\"300\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.1-300x204.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.1.png 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-74848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.2-300x215.png\" alt=\"Big Ideas Math 8th Grade Solution Key Chapter 4 img_9.2\" width=\"300\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.2-300x215.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Solution-Key-Chapter-4-img_9.2.png 611w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 10.<br \/>\nx = 2.5<br \/>\nAnswer:<br \/>\nThe graph of x = 2.5 is a vertical line passing through (2.5, 0)<br \/>\nDraw a vertical line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-75957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-img_10.1-300x198.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 img_10.1\" width=\"300\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-img_10.1-300x198.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-img_10.1.png 533w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nThe graph of y = \\(\\frac{2}{3}\\) is a horizontal line passing through (0, \\(\\frac{2}{3}\\))<br \/>\nDraw a horizontal line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-75965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-4-img_11-300x179.png\" alt=\"BIM Grade 8 Answer Key Chapter 4 img_11\" width=\"300\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-4-img_11-300x179.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answer-Key-Chapter-4-img_11.png 619w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<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-32974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 4\" width=\"393\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-4.png 393w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-4-300x32.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\nAnswer:<br \/>\ny = x &#8211; 2<br \/>\n4x + 3 = y<br \/>\ny = x\u00b2 + 6<br \/>\nx + 5 = y<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. The rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nA game show contestant earns y dollars for completing a puzzle in x minutes. This situation is represented by the equation y = &#8211; 250x + 5000. How long did a contestant who earned $500 take to complete the puzzle? Justify your answer.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA game show contestant earns y dollars for completing a puzzle in x minutes.<br \/>\nThis situation is represented by the equation y = &#8211; 250x + 5000.<br \/>\ny = -250x + 5000<br \/>\n500 = -250x + 5000<br \/>\n500 &#8211; 5000 = -250x + 5000 &#8211; 5000<br \/>\n-4500 = -250x<br \/>\nx = 18<\/p>\n<p>Question 14.<br \/>\nThe total cost y (in dollars) to join a cheerleading team and attend x competitions is represented by the equation y = 10x + 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 5\" width=\"170\" height=\"283\" \/><br \/>\na. Graph the linear equation.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_14-300x242.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 img_14\" width=\"300\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_14-300x242.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_14.png 625w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>b. You have $75 to spend. How many competitions can you attend?<br \/>\nAnswer:<br \/>\n75 \u2264 10x + 50<br \/>\n75 &#8211; 50 \u2264 10x<br \/>\n25 \u2264 10x<br \/>\n2.5 \u2265 x<br \/>\nBy this I can say that I can attend 2 competitions if I have $75 to spend.<\/p>\n<p>Question 15.<br \/>\nThe seating capacity for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need. How many extra tables do you need to double the original seating capacity?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe seating capacity for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.<br \/>\ny = 8x + 56<br \/>\n2 \u00d7 56 = 8x + 56<br \/>\n112 = 8x + 56<br \/>\n8x = 112 &#8211; 56<br \/>\n8x = 56<br \/>\nx = 7 tables<\/p>\n<h3><a id=\"Graphing_Linear_Equations_Homework_&amp;_Practice_4.1\"><\/a>Graphing Linear Equations Homework &amp; Practice 4.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Tell whether the triangles are similar. Explain.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 6\" width=\"198\" height=\"117\" \/><br \/>\nAnswer:<br \/>\nx\u00b0 + 46\u00b0 + 95\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 141\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 141\u00b0<br \/>\nx\u00b0 = 39\u00b0<br \/>\nThus the angles of the triangle are 39\u00b0, 46\u00b0, 95\u00b0<br \/>\ny\u00b0 + 39\u00b0 + 46\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 75\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 75\u00b0<br \/>\ny\u00b0 = 95\u00b0<br \/>\nThree angles of the triangle are 39\u00b0, 46\u00b0, 95\u00b0<br \/>\nThe triangles have two pairs of congruent angles.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 7\" width=\"198\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nx\u00b0 + 40\u00b0 + 51\u00b0 = 180\u00b0<br \/>\nx\u00b0 + 91\u00b0 = 180\u00b0<br \/>\nx\u00b0 = 180\u00b0 &#8211; 91\u00b0<br \/>\nx\u00b0 = 89\u00b0<br \/>\nThree angles of the triangle are 40\u00b0, 51\u00b0, 89\u00b0<br \/>\ny\u00b0 + 40\u00b0 + 79\u00b0 = 180\u00b0<br \/>\ny\u00b0 + 119\u00b0 = 180\u00b0<br \/>\ny\u00b0 = 180\u00b0 &#8211; 119\u00b0<br \/>\ny\u00b0 = 61\u00b0<\/p>\n<p><strong>Describe the translation of the point to its image.<\/strong><br \/>\nQuestion 3.<br \/>\n(1, &#8211; 4) \u2192 (3, 0)<br \/>\nAnswer:<br \/>\nA(1, -4) = A'(1 + 2, -4) = (3, -4)<br \/>\nA'(3, 4) = B(3, -4 + 4) = (3, 0)<br \/>\nTranslate 2 units right and 4 units up.<\/p>\n<p>Question 4.<br \/>\n(6, 4) \u2192 (- 4, &#8211; 6)<br \/>\nAnswer:<br \/>\nWe are given the points<br \/>\n(6, 4) \u2192 (- 4, &#8211; 6)<br \/>\nA(6, 4) = A'(6 &#8211; 10, 4) = (-4, 4)<br \/>\nA'(-4, -4) = B(-4, 4 &#8211; 10) = (-4, -6)<\/p>\n<p>Question 5.<br \/>\n(4, &#8211; 2) \u2192 (- 9, 3)<br \/>\nAnswer:<br \/>\nWe are given the points<br \/>\nA(4, -2)<br \/>\nB(-9, 3)<br \/>\nA(4, -2) = A'(4 &#8211; 13, -2) = (-9, -2)<br \/>\nA'(-9, -2) = B(-9, -2 + 4) = (-9, 3)<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>CREATING GRAPHS<\/strong> Make a graph of the situation. (See Exploration 1, p. 141.)<br \/>\nQuestion 6.<br \/>\nThe equation y = &#8211; 2x + 8 represents the amount (in fluid ounces) of dish detergent in a bottle after x days of use.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_15-294x300.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_15\" width=\"294\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_15-294x300.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_15.png 699w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><\/p>\n<p>Question 7.<br \/>\nThe equation y = 15x + 20 represents the cost (in dollars) of a gym membership after x months.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_16-250x300.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_16\" width=\"250\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_16-250x300.png 250w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_16.png 593w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><\/p>\n<p><strong>PRECISION<\/strong> Copy and complete the table with two solutions. Plot the ordered pairs and draw the graph of the linear equation. Use the graph to find a third solution of the equation.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 8\" width=\"202\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_17-300x259.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_17\" width=\"300\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_17-300x259.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_17.png 696w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n(x, y) = (2, 5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_18-300x259.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_18\" width=\"300\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_18-300x259.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_18.png 696w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 9\" width=\"195\" height=\"80\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_19-300x255.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_19\" width=\"300\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_19-300x255.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_19-768x653.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_19.png 792w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n(x, y) = (3, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-76064 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_20-300x255.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_20\" width=\"300\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_20-300x255.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_20-768x653.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_20.png 792w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>GRAPHING A LINEAR EQUATION<\/strong> Graph the linear equation.<br \/>\nQuestion 10.<br \/>\ny = &#8211; 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_21-263x300.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_21\" width=\"263\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_21-263x300.png 263w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_21.png 507w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><\/p>\n<p>Question 11.<br \/>\ny = 9x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_22-282x300.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_22\" width=\"282\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_22-282x300.png 282w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_22.png 481w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><\/p>\n<p>Question 12.<br \/>\ny = 5<br \/>\nAnswer:<br \/>\nThe graph of y = 5 is a horizontal line passing through (0, 5)<br \/>\nDraw a horizontal line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_23-300x172.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_23\" width=\"300\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_23-300x172.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_23.png 651w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\nx = &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_24-300x199.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_24\" width=\"300\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_24-300x199.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_24.png 537w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\ny = x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_25-300x204.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_25\" width=\"300\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_25-300x204.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_25.png 525w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 15.<br \/>\ny = &#8211; 7x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_26-300x292.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_26\" width=\"300\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_26-300x292.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_26.png 475w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 16.<br \/>\ny = &#8211; \\(\\frac{x}{8}\\) + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_27-300x141.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_27\" width=\"300\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_27-300x141.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_27.png 759w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 17.<br \/>\ny = 0.75x &#8211; 0.5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_28-300x198.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_28\" width=\"300\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_28-300x198.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_28.png 593w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 18.<br \/>\ny = &#8211; \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_29-300x137.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_29\" width=\"300\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_29-300x137.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_29.png 641w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 19.<br \/>\ny = 6.75<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_30-300x200.png\" alt=\"Bigideas math answers grade 8 chapter 4 img_30\" width=\"300\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_30-300x200.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-chapter-4-img_30.png 575w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 20.<br \/>\nx = &#8211; 0.5<br \/>\nAnswer:<br \/>\nThe graph of x = -0.5 is a vertical line passing through (-0.5, 0)<br \/>\nDraw a vertical line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_26-300x243.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_26\" width=\"300\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_26-300x243.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_26.png 517w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 21.<br \/>\nx = \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nThe graph of x = \\(\\frac{1}{4}\\) is a vertical line passing through (\\(\\frac{1}{4}\\), 0)<br \/>\nDraw a vertical line through this point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_27-300x245.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_27\" width=\"300\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_27-300x245.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_27.png 471w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend graphs the equation y = 4. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_28-300x185.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_28\" width=\"300\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_28-300x185.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_28.png 571w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nNo my friend is not correct because the graph for the equation y = 4 is a\u00a0 horizontal line not a vertical line, and it passes through the point (0, 4) not (4, 0)<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe equation y = 20 represents the cost y (in dollars) for sending x text messages in a month. Graph the linear equation. What does the graph tell you about your texting plan?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 10\" width=\"175\" height=\"149\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_29-300x275.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_29\" width=\"300\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_29-300x275.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_29.png 656w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe equation y = 2x + 3 represents the cost y (in dollars) of mailing a package that weighs x pounds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 11\" width=\"204\" height=\"183\" \/><br \/>\na. Use a graph to estimate how much it costs to mail the package.<br \/>\nb. Use the equation to find exactly how much it costs to mail the package.<br \/>\nAnswer:<br \/>\nGiven the equation y = 2x + 3<br \/>\nThe ordered pairs will be (0, 3), (2,7), (4, 11)<br \/>\nNow plot the ordered pairs<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_30-286x300.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_30\" width=\"286\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_30-286x300.png 286w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_30.png 674w\" sizes=\"(max-width: 286px) 100vw, 286px\" \/><br \/>\ny = 2(1.126) + 3<br \/>\n= 5.252 \u2248 5.25<\/p>\n<p><strong>SOLVING A LINEAR EQUATION<\/strong> Solve for y. Then graph the linear equation.<br \/>\nQuestion 25.<br \/>\ny &#8211; 3x = 1<br \/>\nAnswer:<br \/>\ny &#8211; 3x = 1<br \/>\ny = 3x + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_31-300x247.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_31\" width=\"300\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_31-300x247.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_31.png 461w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nDraw a line through the points<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_32-300x211.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_32\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_32-300x211.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_32.png 527w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 26.<br \/>\n5x + 2y = 4<br \/>\nAnswer:<br \/>\n5x + 2y = 4<br \/>\n2y = 4 &#8211; 5x<br \/>\ny = &#8211; \\(\\frac{5}{2}\\)x + 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_33-300x274.png\" alt=\"BIM 8th Grade Solution Key Chapter 4 img_33\" width=\"300\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_33-300x274.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_33.png 511w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 27.<br \/>\n&#8211; \\(\\frac{1}{3}\\)y + 4x = 3<br \/>\nAnswer:<br \/>\n&#8211; \\(\\frac{1}{3}\\)y + 4x = 3<br \/>\n&#8211; \\(\\frac{1}{3}\\)y = 3 &#8211; 4x<br \/>\ny = 12x &#8211; 9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_34-285x300.png\" alt=\"BIM 8th Grade Solution Key Chapter 4 img_34\" width=\"285\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_34-285x300.png 285w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_34.png 531w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/><\/p>\n<p>Question 28.<br \/>\nx + 0.5y = 1.5<br \/>\nAnswer:<br \/>\nx + 0.5y = 1.5<br \/>\n0.5y = -x + 1.5<br \/>\ny = -2x + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_35-300x256.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 4 img_35\" width=\"300\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_35-300x256.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_35.png 623w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe depth y (in inches) of a lake after x years is represented by the equation y = 0.2x + 42. How much does the depth of the lake increase in four years? Use a graph to justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 12\" width=\"201\" height=\"150\" \/><br \/>\nAnswer:<br \/>\ny = 0.2x + 42<br \/>\nDepth of the lake now: y = 0.2(0) + 42 = 42<br \/>\nDepth of the lake after 4 years: y = 0.2(4) + 42 = 42.8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_36-300x264.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 4 img_36\" width=\"300\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_36-300x264.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_36.png 607w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n42.8 &#8211; 42 = 0.8 inches<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe amount y (in dollars) of money in your savings account after x months is represented by the equation y = 12.5x + 100.<br \/>\na. Graph the linear equation.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_37-300x248.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 4 img_37\" width=\"300\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_37-300x248.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_37.png 547w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. How many months will it take you to save a total of $237.50?<br \/>\nAnswer:<br \/>\ny = 12.5x + 100<br \/>\n237.5 = x + 100<br \/>\n237.5 &#8211; 100 = 12.5x + 100 &#8211; 100<br \/>\n12.5x = 137.5<br \/>\nx = 11<\/p>\n<p>Question 31.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe radius y (in millimeters) of a chemical spill after x days is represented by the equation y = 6x + 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.1 13\" width=\"199\" height=\"158\" \/><br \/>\na. Graph the linear equation.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_38-300x261.png\" alt=\"Big Ideas Math Grade 8 Answers Chapter 4 img_38\" width=\"300\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_38-300x261.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_38-768x669.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answers-Chapter-4-img_38.png 818w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. The leak is noticed after two weeks. What is the area of the leak when it is noticed? Justify your answer.<br \/>\nAnswer:<br \/>\ny = 6(14) + 50<br \/>\ny = 84 + 50<br \/>\ny = 134 mm<br \/>\n2\u03c0r = 2\u03c0 = 841.95 sq. mm<\/p>\n<p>Question 32.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe sum S of the interior angle measures of a polygon with n sides is S = (n &#8211; 2) \u2022 180\u00b0.<br \/>\na. Plot four points (n, S) that satisfy the equation. Is the equation a linear equation? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_39-300x213.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_39\" width=\"300\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_39-300x213.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_39-768x544.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_39.png 974w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. Does the value n = 3.5 make sense in the context of the problem? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe value n = 3.5 does not make sense because the number of angles cannot be other than integer greater or equal to 2.<\/p>\n<p>Question 33.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOne second of video on your cell phone uses the same amount of memory as two pictures. Your cell phone can store 2500 pictures.<br \/>\na. Create a graph that represents the number y of pictures your cell phone can store when you take x seconds of video.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-76961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_40-300x242.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_40\" width=\"300\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_40-300x242.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_40-768x620.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_40.png 978w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. How many pictures can your cell phone store in addition to a video that is one minute and thirty seconds long?<br \/>\nAnswer:<br \/>\nDetermine the number of pictures you can store in addition to a video of 1 min 30 seconds.<br \/>\n1 min 30 seconds = (60 + 90) 3 seconds = 90 seconds<br \/>\n2500 &#8211; (2 . 90)<br \/>\n2500 &#8211; 180 = 2320 pictures<\/p>\n<h3><a id=\"Lesson_4.2_Slope_of_a_Line\"><\/a>Lesson 4.2 Slope of a Line<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Measuring the Steepness of a Line<br \/>\nWork with a partner. Draw any nonvertical line in a coordinate plane.<br \/>\na. Develop a way to measure the steepness of the line. Compare your method with other pairs.<br \/>\nb. Draw a line that is parallel to your line. What can you determine about the steepness of each line? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using Right Triangles<br \/>\nWork with a partner. Use the figure shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 1\" width=\"532\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-1.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-1-300x135.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\na. \u25b3ABC is a right triangle formed by drawing a horizontal line segment from point A and a vertical line segment from point B. Use this method to draw another right triangle, \u25b3DEF, with its longest side on the line<br \/>\nb. What can you conclude about the two triangles in part(a)? Justify your conclusion. Compare your results with other pairs.<br \/>\nc. Based on your conclusions in part(b), what is true about \\(\\frac{BC}{AC}\\) and the corresponding measure in \u25b3DEF? Explain your reasoning. What do these values tell you about the line?<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 2\" width=\"188\" height=\"103\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the slope of the line.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 3\" width=\"140\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-2, 3)<br \/>\n(x2, y2) = (3, 2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (2 -3)\/(3 &#8211; (-2))<br \/>\nm = -1\/5<br \/>\nThus slope = -1\/5<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 4\" width=\"150\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-4, -1)<br \/>\n(x2, y2) = (2, 1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (1 &#8211; (-1))\/(2 &#8211; (-4))<br \/>\nm = 2\/6<br \/>\nThus slope = 1\/3<\/p>\n<p><strong>Find the slope of the line through the given points.<\/strong><br \/>\nQuestion 3.<br \/>\n(1, -2), (7, -2)<br \/>\nAnswer:<br \/>\n(x1, y1) = (1, -2)<br \/>\n(x2, y2) = (7, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; (-2))\/(7 &#8211; 1)<br \/>\nm = 0\/6<br \/>\nThus slope = 0<\/p>\n<p>Question 4.<br \/>\n(-3, -3), (-3, -5)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-3, -3)<br \/>\n(x2, y2) = (-3, -5)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-5 + 3)\/(-3 + 3)<br \/>\nm = -2\/0<br \/>\nThus slope = undefined<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF<\/strong><br \/>\nThe blue line passes through (-4, -3) and (-3, 2). Are any of the lines parallel? Explain.<br \/>\nAnswer:<br \/>\n(x1, y1) = (-4, -3)<br \/>\n(x2, y2) = (-3, 2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (2 + 3)\/(-3 + 4)<br \/>\nm = 5\/1<br \/>\nm = 5<br \/>\nThe slpe of the blue line is 5 and the slope of the red line is also 5.<br \/>\nThe blue lines and red lines have same slopes so they are parallel.<\/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 6.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat does it mean for a line to have a slope of 4?<br \/>\nAnswer:<br \/>\nIf a line have a slope of 4 it means that the line rises 4 units for every 1 units it runs.<\/p>\n<p><strong>FINDING THE SLOPE OF A LINE<\/strong> Find the slope of the line through the given points.<br \/>\nQuestion 7.<br \/>\n(1, -1), (6, 2)<br \/>\nAnswer:<br \/>\n(x1, y1) = (1, -1)<br \/>\n(x2, y2) = (6, 2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (2 &#8211; (-1))\/(6 &#8211; 1)<br \/>\nm = 3\/5<\/p>\n<p>Question 8.<br \/>\n(2, -3), (5, -3)<br \/>\nAnswer:<br \/>\n(x1, y1) = (2, -3)<br \/>\n(x2, y2) = (5, -3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (5 &#8211; 2)\/(-3 + 3)<br \/>\nm = 3\/0<br \/>\nm = undefined<\/p>\n<p>Question 9.<br \/>\n<strong>FINDING SLOPE<\/strong><br \/>\nAre the lines parallel? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 5\" width=\"161\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nRed line:<br \/>\n(x1, y1) = (-1, 0)<br \/>\n(x2, y2) = (1, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 0)\/1 &#8211; (-1))<br \/>\nm = -2\/2<br \/>\nm = -1<br \/>\nBlue Line:<br \/>\n(x1, y1) = (-1, 3)<br \/>\n(x2, y2) = (1, -1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; 3)\/(1 &#8211; (-1))<br \/>\nm = -4\/2<br \/>\nm = -2<br \/>\nThe slope of the blue line and red line are not the same. So they are not parallel.<\/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 10.<br \/>\nThe table shows the lengths (in inches) of your hair months after your last haircut. The points in the table lie on a line. Find and interpret the slope of the line. After how many months is your hair 4 inches long?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 6\" width=\"106\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nDetermine the slope of the line using two points from the table:<br \/>\n(2, 1), (4, 2)<br \/>\nm = (2 &#8211; 1)\/4 &#8211; 2<br \/>\nm = 1\/2<br \/>\nm = 0.5<br \/>\nThis means that each month the hair grows 0.5 inches<br \/>\nAs the hair grows 0.5 inches\/ month, it will be 4 inches long after 4\/0.5 = 8 months.<\/p>\n<p>Question 11.<br \/>\nA customer pays an initial fee and a daily fee to rent a snowmobile. The total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars. What is the daily fee? Justify your answer.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA customer pays an initial fee and a daily fee to rent a snowmobile.<br \/>\nThe total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars.<br \/>\nm = (120 &#8211; 92)\/5 &#8211; 3<br \/>\nm = 28\/2<br \/>\nm = 14<\/p>\n<p>Question 12.<br \/>\nYou in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes. Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour. Compare your rates of change in elevation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 7\" width=\"194\" height=\"169\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes.<br \/>\nYour friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour.<br \/>\n(750 &#8211; 720)\/30 = 30\/30 = 1 ft\/min<br \/>\n(690 &#8211; 600)\/60 = 90\/60 = 1.5 ft\/min<\/p>\n<h3><a id=\"Slope_of_a_Line_Homework_&amp;_Practice_4.2\"><\/a>Slope of a Line Homework &amp; Practice 4.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 4x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_41-300x286.png\" alt=\"Big Ideas Math Grade 8 Chapter 4 Solution Key img_41\" width=\"300\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_41-300x286.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_41.png 619w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\nx = -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_42-300x217.png\" alt=\"Big Ideas Math Grade 8 Chapter 4 Solution Key img_42\" width=\"300\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_42-300x217.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_42.png 519w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\ny = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_43-300x214.png\" alt=\"Big Ideas Math Grade 8 Chapter 4 Solution Key img_43\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_43-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_43.png 569w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\ny = \\(\\frac{3}{2}\\)x &#8211; \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_44-300x247.png\" alt=\"Big Ideas Math Grade 8 Chapter 4 Solution Key img_44\" width=\"300\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_44-300x247.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Solution-Key-img_44.png 573w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Find the missing values in the ratio table.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 8\" width=\"225\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-77574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-8-1.png\" alt=\"Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-8\" width=\"225\" height=\"64\" \/><br \/>\nx\/10 = 1\/3<br \/>\nx = 10\/3<br \/>\nx = 3.33<br \/>\n1\/3 = 5\/y<br \/>\ny = 5 \u00d7 3<br \/>\ny = 15<br \/>\n1\/3 = 7\/z<br \/>\nz = 3 \u00d7 7<br \/>\nz = 21<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 9\" width=\"221\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-77589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-9-1.png\" alt=\"Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-9\" width=\"221\" height=\"67\" \/><\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>USING RIGHT TRIANGLES<\/strong> Use the figure shown (See Exploration 2, p. 147.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 10\" width=\"182\" height=\"115\" \/><br \/>\nQuestion 7.<br \/>\nFind the slope of the line.<br \/>\nAnswer:<br \/>\n(x1, y1) = B(-4, 2)<br \/>\n(x2, y2) = A(-2, 1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (1 &#8211; 2)\/(-2 &#8211; (-4))<br \/>\nm = -1\/2<br \/>\nThus the slope m = -1\/2<\/p>\n<p>Question 8.<br \/>\nLet point D be at (-4, 1). Use the sides of \u25b3BDA to find the slope of the line.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Answers-img_45-300x219.png\" alt=\"Big Ideas Math Grade 8 Chapter 4 Answers img_45\" width=\"300\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Answers-img_45-300x219.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Answers-img_45-768x562.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Chapter-4-Answers-img_45.png 871w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nm = -BD\/DA = -1\/2<\/p>\n<p><strong>FINDING THE SLOPE OF A LINE<\/strong> Find the slope of the line.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 11\" width=\"136\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-2, 0)<br \/>\n(x2, y2) = (2, 3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (3 &#8211; 0)\/(2 &#8211; (-2))<br \/>\nm = 3\/4<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 11\" width=\"154\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-2, 5)<br \/>\n(x2, y2) = (2, 0)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (0 &#8211; 5)\/(2 &#8211; (-2))<br \/>\nm = -5\/4<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 13\" width=\"139\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-4, 1)<br \/>\n(x2, y2) = (1, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 1)\/(1 + 2)<br \/>\nm = -3\/5<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 14\" width=\"150\" height=\"139\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-5, -4)<br \/>\n(x2, y2) = (1, -3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-3 &#8211; (-4))\/(1 &#8211; (-5))<br \/>\nm = 1\/6<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 15\" width=\"144\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-1, 3)<br \/>\n(x2, y2) = (3, 3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (3 &#8211; 3)\/(3 &#8211; (-1))<br \/>\nm = 0\/4<br \/>\nm = 0<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 16\" width=\"143\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (1, 3)<br \/>\n(x2, y2) = (1, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 3)\/(1 &#8211; 1)<br \/>\nm = -5\/0<br \/>\nm = undefined<\/p>\n<p><strong>FINDING THE SLOPE OF A LINE<\/strong> Find the slope of the line through the given points.<br \/>\nQuestion 15.<br \/>\n(4, -1), (-2, -1)<br \/>\nAnswer:<br \/>\n(x1, y1) = (4, -1)<br \/>\n(x2, y2) = (-2, -1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; (-1))\/(-2 &#8211; 4)<br \/>\nm = 0\/-6<br \/>\nm = 0<\/p>\n<p>Question 16.<br \/>\n(5, -3), (5, 8)<br \/>\nAnswer:<br \/>\n(x1, y1) = (5, -3)<br \/>\n(x2, y2) = (5, 8)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (8 &#8211; 3)\/(5 &#8211; 5)<br \/>\nm = 5\/0<br \/>\nm = undefined<\/p>\n<p>Question 17.<br \/>\n(-7, 0), (-7, -6)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-7, 0)<br \/>\n(x2, y2) = (-7, -6)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-6 &#8211; 0)\/(-7 &#8211; (-7))<br \/>\nm = -6\/0<br \/>\nm = undefined<\/p>\n<p>Question 18.<br \/>\n(-3, 1), (-1, 5)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-3, 1)<br \/>\n(x2, y2) = (-1, 5)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (5 &#8211; 1)\/(-1 + 3)<br \/>\nm = 4\/2<br \/>\nm = 2<\/p>\n<p>Question 19.<br \/>\n(10, 4), (4, 15)<br \/>\nAnswer:<br \/>\n(x1, y1) = (10, 4)<br \/>\n(x2, y2) = (4, 15)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (15 &#8211; 4)\/(4 &#8211; 10)<br \/>\nm = 11\/-6<br \/>\nm = -11\/6<\/p>\n<p>Question 20.<br \/>\n(-3, 6), (2, 6)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-3, 6)<br \/>\n(x2, y2) = (2, 6)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (6 &#8211; 6)\/(2 &#8211; (-3))<br \/>\nm = 0\/5<br \/>\nm = 0<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nDraw a line through each point using slope of m = \\(\\frac{1}{4}\\). Do the lines intersect? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 17\" width=\"141\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_46-300x253.png\" alt=\"Big Ideas math Grade 8 Answer Key Chapter 4 img_46\" width=\"300\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_46-300x253.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_46-768x649.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_46.png 842w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe 2 lines are parallel because they have the same slope and they do not intersect.<\/p>\n<p>Question 22.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the slope of the line shown. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 18\" width=\"232\" height=\"162\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_47-300x285.png\" alt=\"Big Ideas math Grade 8 Answer Key Chapter 4 img_47\" width=\"300\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_47-300x285.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-math-Grade-8-Answer-Key-Chapter-4-img_47.png 475w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nNo my friend is not correct because the denominator should be 2 &#8211; 4<br \/>\n(x1, y1) = (2, 3)<br \/>\n(x2, y2) = (4, 1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (1 &#8211; 3)\/(4 &#8211; 2)<br \/>\nm = -2\/2<br \/>\nm = -1<\/p>\n<p><strong>IDENTIFYING PARALLEL LINES<\/strong> Which lines are parallel? How do you know?<br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 19\" width=\"207\" height=\"142\" \/><br \/>\nAnswer:<br \/>\nBlue line:<br \/>\n(x1, y1) = (-5, 2)<br \/>\n(x2, y2) = (-4, -1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; 2)\/(-4 &#8211; (-5))<br \/>\nm = -3\/1<br \/>\nm = -3<br \/>\nRed line:<br \/>\n(x1, y1) = (-2, 1)<br \/>\n(x2, y2) = (-1, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 1)\/(-1 &#8211; (-2))<br \/>\nm = -3\/1<br \/>\nm = -3<br \/>\nGreen Line:<br \/>\n(x1, y1) = (1, 3)<br \/>\n(x2, y2) = (2, -1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; 3)\/(2 &#8211; 1)<br \/>\nm = -4\/1<br \/>\nm = -4<br \/>\nBlue line and red line have slope of -3, so they are parallel.<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 20\" width=\"212\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nBlue line:<br \/>\n(x1, y1) = (-2, 3)<br \/>\n(x2, y2) = (-5, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 3)\/(-5 &#8211; (-2))<br \/>\nm = -5\/-3<br \/>\nm = 5\/3<br \/>\nRed line:<br \/>\n(x1, y1) = (1, 2)<br \/>\n(x2, y2) = (-2, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 2)\/(-2 &#8211; 1)<br \/>\nm = -4\/-3<br \/>\nm = 4\/3<br \/>\nGreen Line:<br \/>\n(x1, y1) = (4, 1)<br \/>\n(x2, y2) = (1, -3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-3 &#8211; 1)\/(1 &#8211; 4)<br \/>\nm = -4\/-3<br \/>\nm = 4\/3<br \/>\nRed line and green line have slope of 4\/3 by this we can say that they are parallel.<\/p>\n<p><strong>IDENTIFYING PARALLEL LINES<\/strong> Are the given lines parallel? Explain your reasoning.<br \/>\nQuestion 25.<br \/>\ny = -5, y = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_47-300x267.png\" alt=\"8th Grade Big Ideas Math Answers Chapter 4 img_47\" width=\"300\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_47-300x267.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_47.png 643w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nBoth lines are horizontal and have slope = 0<\/p>\n<p>Question 26.<br \/>\ny = 0, x = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_48-300x250.png\" alt=\"8th Grade Big Ideas Math Answers Chapter 4 img_48\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_48-300x250.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_48.png 561w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line y = 0 have slope = 0 and are horizontal lines.<br \/>\nThe line x = 0 have slope = undefined and are vertical lines.<br \/>\nSo, they are not parallel.<\/p>\n<p>Question 27.<br \/>\nx = -4, x = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-77680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_49-300x207.png\" alt=\"8th Grade Big Ideas Math Answers Chapter 4 img_49\" width=\"300\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_49-300x207.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answers-Chapter-4-img_49.png 585w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nBoth lines are vertical and have an undefined slope.<\/p>\n<p><strong>FINDING SLOPE<\/strong> The points in the table lie on a line. Find the slope of the line.<br \/>\nQuestion 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 21\" width=\"209\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (10 &#8211; 2)\/(3 &#8211; 1) = (18 &#8211; 10)\/(5 &#8211; 3) = (26 &#8211; 18)\/(7 &#8211; 5)<br \/>\nm = 8\/2 = 8\/2 = 8\/2<br \/>\nm = 4 = 4 = 4<br \/>\nSlope = 4<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-22.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 22\" width=\"198\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (2 &#8211; 0)\/(2 &#8211; (-3)) = (4 &#8211; 2)\/(7 &#8211; 2) = (6 &#8211; 4)\/(12 &#8211; 7)<br \/>\nm = 2\/5 = 2\/5 = 2\/5<br \/>\nm = 2\/5<\/p>\n<p>Question 30.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nCarpenters refer to the slope of a roof as the pitch of the roof. Find the pitch of the roof.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-23.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 23\" width=\"203\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nPitch of the roof = rise\/run<br \/>\n= 4\/12 = 1\/3<\/p>\n<p>Question 31.<br \/>\n<strong>PROJECT<\/strong><br \/>\nThe guidelines for a wheelchair ramp suggest that the ratio of the rise to the run be no greater than 1 : 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-24.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 24\" width=\"194\" height=\"270\" \/><br \/>\na. CHOOSE TOOLS Find a wheelchair ramp in your school or neighborhood. Measure its slope. Does the ramp follow the guidelines?<\/p>\n<p>Answer:<br \/>\nrise\/run &lt; 1\/12<br \/>\nm = 0.06<br \/>\n1\/12 = 0.0833<br \/>\n0.06 &lt; 0.0833<br \/>\nAs m &lt; 1\/12 the wheelchair ramp follows the guides.<\/p>\n<p>b. Design a wheelchair ramp that provides access to a building with a front door that is 2.5 feet above the sidewalk. Illustrate your design.<br \/>\nAnswer:<br \/>\nAC\/AB = 1\/12<br \/>\n2.5\/AB = 1\/12<br \/>\nAB = 2.5 \u00d7 12<br \/>\nAB = 30<br \/>\nSo the end of the ramp should be placed at least 30 feet from the front door.<\/p>\n<p><strong>USING AN EQUATION<\/strong> Use an equation to find the value of k so that the line that passes through the given points has the given slope.<br \/>\nQuestion 32.<br \/>\n(1, 3), (5, k); m = 2<br \/>\nAnswer:<br \/>\nA(1, 3)<br \/>\nB(5, k)<br \/>\nm = 2<br \/>\n2 = (k &#8211; 3)\/(5 &#8211; 1)<br \/>\n2 \u00d7 4 = k &#8211; 3<br \/>\n8 = k &#8211; 3<br \/>\nk = 8 + 3<br \/>\nk = 11<\/p>\n<p>Question 33.<br \/>\n(-2, k), (2, 0); m = -1<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA(-2, k)<br \/>\nB(2, 0)<br \/>\nm = -1<br \/>\n-1 = (0 &#8211; k)\/2 &#8211; (-2)<br \/>\n-1 = -k\/4<br \/>\n-4 = -k<br \/>\nk = 4<\/p>\n<p>Question 34.<br \/>\n(-4, k), (6, -7); m = &#8211;\\(\\frac{1}{5}\\)<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA(-4, k)<br \/>\nB(6, -7)<br \/>\nm = &#8211;\\(\\frac{1}{5}\\)<br \/>\n&#8211;\\(\\frac{1}{5}\\) = (-7 &#8211; k)\/6 &#8211; (-4)<br \/>\n-2 = -7 &#8211; k<br \/>\n-2 + 7 = -k<br \/>\n5 = -k<br \/>\nk = -5<\/p>\n<p>Question 35.<br \/>\n(4, -4), (k, -1); m = \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{3}{4}\\) = (-1 &#8211; (-4))\/(k &#8211; 4)<br \/>\n4 = k &#8211; 4<br \/>\nk = 4 + 4<br \/>\nk = 8<\/p>\n<p>Question 36.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe graph shows the numbers of prescriptions filled over time by a pharmacy.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-25.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 25\" width=\"232\" height=\"163\" \/><br \/>\na. Find the slope of the line.<br \/>\nAnswer:<br \/>\n(0, 0), (20, 5)<br \/>\nm = (5 &#8211; 0)\/(20 &#8211; 0)<br \/>\nm = 5\/20<br \/>\nm = 1\/4<br \/>\nb. Explain the meaning of the slope as a rate of change.<br \/>\nAnswer:<br \/>\nThis means that every 4 minutes a prescription is filled.<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWhich is steeper: the boatramp, or a road with a 12% grade? Note: Explain. (Road grade is the vertical increase divided by the horizontal distance.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-26.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 26\" width=\"281\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nMramp = rise\/run = 6\/36 = 1\/6<br \/>\nMroad = 12% = 12\/100 = 0.12<br \/>\n0.16 = 0.166&#8230; &gt; 0.12<br \/>\nMramp &gt; Mroad<br \/>\nTherefore the slope of the ramp is steeper than the slope of the road.<\/p>\n<p>Question 38.<br \/>\n<strong>REASONING<\/strong><br \/>\nDo the points A(-2, -1), B(1, 5), and C(4, 11) lie on the same line? Without using a graph, how do you know?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA(-2, -1), B(1, 5), and C(4, 11)<br \/>\nmAB = (5 &#8211; (-1))\/(1 &#8211; (-2)) = 6\/3 = 2<br \/>\nmBC = (11 &#8211; 5)\/(4 &#8211; 1) = 6\/3 = 2<br \/>\nBy seeing the slopes we can say that the points A, B, C lie on the same line.<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period? Justify your answer.<br \/>\nAnswer:<br \/>\nPjan = 6500<br \/>\nPmay = 17,500<br \/>\nPmay &#8211; Pjan\/5 &#8211; 1<br \/>\n= (17,500 &#8211; 6500)\/4<br \/>\n= 11,000\/4 = 2750<\/p>\n<p>Question 40.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nChoose two points in the coordinate plane. Use the slope formula to find the slope of the line that passes through the two points. Then find the slope using the formula \\(\\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\\). Compare your results.<br \/>\nAnswer:<br \/>\nP1(2, 5)<br \/>\nP2(3, 10)<br \/>\nm1 = (10 &#8211; 5)\/(3 &#8211; 2) = 5\/1 = 5<br \/>\nm2 = (5 &#8211; 10)\/(1 &#8211; 3) = -5\/-1 = 5<br \/>\nm1 = m2<\/p>\n<p>Question 41.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe top and the bottom of the slide are level with the ground, which has a slope of 0.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.2-27.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.2 27\" width=\"260\" height=\"205\" \/><br \/>\na. What is the slope of the main portion of the slide?<br \/>\nb. Describe the change in the slope when the bottom of the slide is only 12 inches above the ground. Explain your reasoning.<br \/>\nAnswer:<br \/>\n18 inches = 1.5 feet<br \/>\nmMC = rise\/run = (8 &#8211; 1.5)\/(12 &#8211; 1 &#8211; 1) = 6.5\/10 = 0.65<br \/>\nAD = 1<br \/>\nmMC = CR\/MR<br \/>\n= (8 &#8211; 1)\/(12 &#8211; 1 &#8211; 1) = 7\/10 = 0.7<br \/>\nThe slope increases from 0.65 to 0.70 because the rise increasses, while the run stays the same.<\/p>\n<h3><a id=\"Lesson_4.3_Graphing_Proportional_Relationships\"><\/a>Lesson 4.3 Graphing Proportional Relationships<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Ratio Table to Find Slope<br \/>\nWork with a partner. The graph shows amounts of vinegar and water that can be used to make a cleaning product.<br \/>\na. Use the graph to make a ratio table relating the quantities. Explain how the slope of the line is represented in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 1\" width=\"229\" height=\"184\" \/><br \/>\nb. Make a ratio table that represents a different ratio of vinegar to water. Use the table to describe the slope of the graph of the new relationship.<br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Deriving an Equation<br \/>\nWork with a partner. Let (x, y) represent any point on the graph of a proportional relationship.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 2\" width=\"411\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-2.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-2-300x141.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><br \/>\na. Describe the relationship between the corresponding side lengths of the triangles shown in the graph. Explain your reasoning.<br \/>\nb. Use the relationship in part(a) to write an equation relating y, m, and x. Then solve the equation for y. How can you find the side lengths of the triangles in the graph?<br \/>\nc. What does your equation in part(b) describe? What does represent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nWHAT IF<br \/>\nThe cost of frozen yogurt is represented by y = 0.75x. Graph the equation and interpret the slope.<br \/>\nAnswer:<br \/>\nThe equation shows that the slope m is 0.75. So the graph passes through the points (0, 0) and (1, 0.75).<br \/>\nPlot the ordered pairs and draw the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_48-300x261.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_48\" width=\"300\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_48-300x261.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_48.png 716w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe slope indicates that the unit cost is $0.75 per ounce.<\/p>\n<p>Question 2.<br \/>\nHow much would a spacecraft that weighs 3500 kilograms on Earth weigh on Titan?<br \/>\nAnswer:<br \/>\ny = 1\/7 x<br \/>\ny = 1\/7 \u00d7 3500<br \/>\ny = 500 kg<br \/>\nSo a spacecraft would weigh 500 kg on Titan.<\/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>GRAPHING A PROPORTIONAL RELATIONSHIP<\/strong> Graph the equation.<br \/>\nQuestion 3.<br \/>\ny = 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_49-284x300.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_49\" width=\"284\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_49-284x300.png 284w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_49.png 614w\" sizes=\"(max-width: 284px) 100vw, 284px\" \/><\/p>\n<p>Question 4.<br \/>\ny = -3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_50-300x300.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_50\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_50-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_50-150x150.png 150w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\ny = 8x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_51-236x300.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_51\" width=\"236\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_51-236x300.png 236w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_51.png 585w\" sizes=\"(max-width: 236px) 100vw, 236px\" \/><\/p>\n<p>Question 6.<br \/>\n<strong>WRITING AND USING AN EQUATION<\/strong><br \/>\nThe number of objects a x machine produces is proportional to the time (in minutes) that the machine runs. The machine produces five objects in four minutes.<br \/>\na. Write an equation that represents the situation.<\/p>\n<p>Answer:<br \/>\nAs 5 objects are produced in 4 minutes, the slope of the line is m = 5\/4.<br \/>\nThe equation that represents the situation is<br \/>\ny = 5\/4 x<br \/>\ny = 1.25 x<\/p>\n<p>b. Graph the equation in part (a) and interpret the slope.<\/p>\n<p>Answer:<br \/>\nUse the slope. The equation shows that the slope m is 1.25. So the graph passes through the points (0, 0) and (1, 1.25)<\/p>\n<p>c. How many objects does the machine produce in one hour?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_52-300x300.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_52\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_52-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_52-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_52.png 643w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/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 7.<br \/>\nThe amount y (in liters) of water that flows over a natural waterfall in x seconds is represented by the equation y = 500x. The graph shows the number of liters of water that flow over an artificial waterfall. Which waterfall has a greater flow? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 3\" width=\"184\" height=\"228\" \/><br \/>\nAnswer:<br \/>\nGiven the equation y = 500x<br \/>\n15000 &#8211; 3000 = 12000<br \/>\n12000\/4 = 3000<br \/>\nMnatural = 500<br \/>\n3000 &gt; 500<br \/>\nTherefore the artificial waterfall has greater flow.<\/p>\n<p>Question 8.<br \/>\nThe speed of sound in air is 343 meters per second. You see lightning and hear thunder 12 seconds later.<br \/>\na. Is there a proportional relationship between the amount of time that passes and your distance from a lightning strike? Explain.<\/p>\n<p>Answer:<br \/>\ny = kx<br \/>\nwhere k is the speed of sound, x the time and y the distance.<br \/>\nYes, there is a proportional relationship between the amount of time that passes and your distance from the lightning strike as the further you are, the more time will pass until the sound reaches you.<\/p>\n<p>b. Estimate your distance from the lightning strike.<br \/>\nAnswer:<br \/>\ny = 343 \u00d7 12<br \/>\n= 4116 meters<\/p>\n<h3><a id=\"Graphing_Proportional_Relationships_Homework_&amp;_Practice_4.3\"><\/a>Graphing Proportional Relationships Homework &amp; Practice 4.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the slope of the line.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 4\" width=\"137\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (0, -3)<br \/>\n(x2, y2) = (3, 0)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (0 &#8211; (-3))\/(3 &#8211; 0)<br \/>\nm = (0 + 3)\/(3 &#8211; 0)<br \/>\nm = 3\/3<br \/>\nm = 1<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 5\" width=\"143\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (0, 1)<br \/>\n(x2, y2) = (3, -5)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-5 &#8211; 1)\/(3 &#8211; 0)<br \/>\nm = -6\/3<br \/>\nm = -2<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 6\" width=\"153\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (0, 0)<br \/>\n(x2, y2) = (2, 8)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (8 &#8211; 0)\/(2 &#8211; 0)<br \/>\nm = 8\/2<br \/>\nm = 4<\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 4.<br \/>\n2x + 3x = 10<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n2x + 3x = 10<br \/>\n5x = 10<br \/>\nx = 10\/5<br \/>\nx = 2<\/p>\n<p>Question 5.<br \/>\nx + \\(\\frac{1}{6}\\) = 4 &#8211; 2x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx + \\(\\frac{1}{6}\\) = 4 &#8211; 2x<br \/>\nx + 2x = 4 &#8211; \\(\\frac{1}{6}\\)<br \/>\n3x = 4 &#8211; \\(\\frac{1}{6}\\)<br \/>\n3x = \\(\\frac{23}{6}\\)<br \/>\nx = \\(\\frac{23}{18}\\)<\/p>\n<p>Question 6.<br \/>\n2(1 &#8211; x) = 11<br \/>\nAnswer:<br \/>\n2(1 &#8211; x) = 11<br \/>\n2 &#8211; 2x = 11<br \/>\n2 &#8211; 11 = 2x<br \/>\n2x = -9<br \/>\nx = -9\/2<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING EQUIVALENT RATIOS<\/strong> The graph shows amounts of water and flour that can be used to make dough. (See Exploration 1, p. 155.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 7\" width=\"158\" height=\"224\" \/><br \/>\nQuestion 7.<br \/>\nUse the graph to make a ratio table relating the quantities. Explain how the slope of the line is represented in the table.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_53-300x106.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_53\" width=\"300\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_53-300x106.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_53.png 451w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nm = rise\/run<br \/>\n= (10 &#8211; 5)\/(6 &#8211; 3)<br \/>\n= 5\/3<br \/>\nThat means to every 5 cups of flour there is an increase of 3 cups of water.<br \/>\nThe slope m is 5\/3.<\/p>\n<p>Question 8.<br \/>\nMake a ratio table that represents a different ratio of flour to water. Use the table to describe the slope of the graph of the new relationship.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_54-300x106.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_54\" width=\"300\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_54-300x106.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_54.png 451w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFrom the table we find that for every increase of 7 cups of flour there is an increase of 4 cups of water.<br \/>\nThe slope is 7\/4.<\/p>\n<p>Question 9.<br \/>\n<strong>GRAPHING AN EQUATION<\/strong><br \/>\nThe amount y(in dollars) that you raise by selling fundraiser tickets is represented by the equation y = 5x. Graph the equation and interpret the slope.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_55-215x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_55\" width=\"215\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_55-215x300.png 215w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_55.png 514w\" sizes=\"(max-width: 215px) 100vw, 215px\" \/><br \/>\nThe slope indicates that the unit cost is $5 per ticket.<\/p>\n<p><strong>IDENTIFYING PROPORTIONAL RELATIONSHIPS<\/strong> Tell whether and are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.<br \/>\nQuestion 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 8\" width=\"160\" height=\"152\" \/><br \/>\nAnswer:<br \/>\nThe graph doesn&#8217;t represent a proportional relationship because it doesn&#8217;t pass through the point (0, 0).<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 9\" width=\"160\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe graph represents a proportional relationship because it is linear and passes through the point (0, 0)<br \/>\n(0, 0), (2, 8)<br \/>\nm = (8 &#8211; 0)\/(2 &#8211; 0)<br \/>\nm = 8\/2<br \/>\nm = 4<br \/>\nThe equation is y = 4x<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 10\" width=\"170\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n(2 &#8211; 1)\/(6 &#8211; 3) = 1\/3<br \/>\n(3 &#8211; 2)\/(9 &#8211; 6) = 1\/3<br \/>\n(4 &#8211; 3)\/(12 &#8211; 9) = 1\/3<br \/>\nAs the rate of change is constant, it means that the graph is a line.<br \/>\n(1 &#8211; y)\/(3 &#8211; 0) = 1\/3<br \/>\n(1 &#8211; y)\/3 = 1\/3<br \/>\n1 &#8211; y = 1<br \/>\ny = 1 &#8211; 1<br \/>\ny = 0<br \/>\nTherefore the point (0, 0) belomgs to the graph.<br \/>\nSo the table represents a proportional relationship<br \/>\ny = 1\/3 x<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 11\" width=\"180\" height=\"66\" \/><br \/>\nAnswer:<br \/>\n(8 &#8211; 4)\/(5 &#8211; 2) = 4\/3<br \/>\n(13 &#8211; 8)\/(8 &#8211; 5) = 5\/3<br \/>\n(23 &#8211; 13)\/10 &#8211; 8 = 10\/2 = 5<\/p>\n<p>Question 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 12\" width=\"273\" height=\"183\" \/><br \/>\na. Write an equation that represents the situation.<br \/>\nb. Interpret the slope of the graph of the equation.<br \/>\nc. How much does it cost to rent the kayak for 5 hours? Justify your answer.<br \/>\nAnswer:<br \/>\ny = kx<br \/>\n27 = k \u00d7 3<br \/>\nk = 27\/3<br \/>\nk = 9<br \/>\nThe equation is k = 9x<br \/>\nb. The slope k = 3 shows that the cost of renting the kayak per hour is $9.<br \/>\nc. y = 9 \u00d7 5<br \/>\ny = 45<\/p>\n<p>Question 15.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe distance y (in miles) that a truck travels on x gallons of gasoline is represented by the equation y = 18x. The graph shows the distance that a car travels.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 13\" width=\"173\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-13.png 173w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-13-150x150.png 150w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><br \/>\na. Which vehicle gets better gas mileage? Explain how you found your answer.<\/p>\n<p>Answer:<br \/>\ny = 18x<br \/>\n(0, 0), (2, 50)<br \/>\nm = (50 &#8211; 0)\/(2 &#8211; 0)<br \/>\nm = 50\/2<br \/>\nm = 25<br \/>\n25 &gt; 18<br \/>\nTherefore the car has better mileage.<\/p>\n<p>b. How much farther can the vehicle you chose in part(a) travel on 8 gallons of gasoline?<br \/>\nAnswer:<br \/>\ny = 25 \u00d7 8 &#8211; 18 \u00d7 8<br \/>\n= 200 &#8211; 144<br \/>\n= 56 miles<\/p>\n<p>Question 16.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nToenails grow about 13 millimeters per year. The table shows fingernail growth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 14\" width=\"275\" height=\"83\" \/><br \/>\na. Do fingernails or toenails grow faster? Explain.<\/p>\n<p>Answer:<br \/>\ny = 0.25x<br \/>\nm = (1.4 &#8211; 0.7)\/(2 &#8211; 1)<br \/>\nm = 0.7<br \/>\ny = 0.7x<br \/>\nBecause 0.7 &gt; 0.25, the fingernails grow faster.<\/p>\n<p>b. In the same coordinate plane, graph equations that represent the growth rates of toenails and fingernails. Compare and interpret the steepness of each graph.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_57-300x246.png\" alt=\"BIM Answer Key Grade 8 Chapter 4 img_57\" width=\"300\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_57-300x246.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_57-768x629.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_57.png 832w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 17.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe quantities and are in a proportional relationship. What do you know about the ratio of y to x for any point (x, y) on the graph of x and y?<br \/>\nAnswer:<br \/>\ny = kx<br \/>\nwhere k is constant<br \/>\ny\/x = k<br \/>\nThis means the ratio of y to x is constant.<\/p>\n<p>Question 18.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe graph relates the temperature change y (in degrees Fahrenheit) to the altitude change x (in thousands of feet).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.3-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.3 15\" width=\"249\" height=\"230\" \/><br \/>\na. Is the relationship proportional? Explain.<\/p>\n<p>Answer: The relationship is proportional because the graph is linear and passes through the origin.<\/p>\n<p>b. Write an equation of the line. Interpret the slope.<\/p>\n<p>Answer:<br \/>\n(0,0), (10, -35)<br \/>\nm = (-35 &#8211; 0)\/(10 &#8211; 0)<br \/>\n= -35\/10<br \/>\n= -3.5<br \/>\ny = -3.5x<\/p>\n<p>c. You are at the bottom of a mountain where the temperature is 74\u00b0F. The top of the mountain is 5500 feet above you. What is the temperature at the top of the mountain? Justify your answer.<br \/>\nAnswer:<br \/>\nx = 5.5 &#8211; 0 = 5.5 thousand feet<br \/>\ny = -3.5x = -3.5(5.5) = -19.25<br \/>\n74 &#8211; 19.25 = 54.75\u00b0F<\/p>\n<p>Question 19.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nConsider the distance equation d = rt, where d is the distance (in feet), r is the rate (in feet per second), and t is the time (in seconds). You run for 50 seconds. Are the distance you run and the rate you run at proportional? Use a graph to justify your answer.<br \/>\nAnswer:<br \/>\nd = rt<br \/>\nd = 50r<br \/>\nHaving the form y = kx the equation represents a proportional relationship.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_58-289x300.png\" alt=\"BIM Answer Key Grade 8 Chapter 4 img_58\" width=\"289\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_58-289x300.png 289w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answer-Key-Grade-8-Chapter-4-img_58.png 738w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/p>\n<h3><a id=\"Lesson_4.4_Graphing_Linear_Equations_in_Slope_Intercept_Form\"><\/a>Lesson 4.4 Graphing Linear Equations in Slope-Intercept Form<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Deriving an Equation<br \/>\nWork with a partner. In the previous section, you learned that the graph of a proportional relationship can be represented by the equation y = mx, where m is the constant of proportionality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 1\" width=\"218\" height=\"173\" \/><br \/>\na. You translate the graph of a proportional relationship 3 units up as shown below. Let (x, y) represent any point on the graph. Make a conjecture about the equation of the line. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 2\" width=\"459\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-2.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-2-300x142.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><br \/>\nb. Describe the relationship between the corresponding side lengths of the triangles. Explain your reasoning.<br \/>\nc. Use the relationship in part(b) to write an equation relating y, m, and x. Does your equation support your conjecture in part(a)? Explain.<br \/>\nd. You translate the graph of a proportional relationship b units up. Write an equation relating y, m, x, and b. Justify your answer.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 3\" width=\"194\" height=\"117\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Find the slope and the y-intercept of the graph of the linear equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 3x &#8211; 7<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 3x &#8211; 7<br \/>\nWrite the equation in slope &#8211; intercept form: y = mx + b<br \/>\nThe slope of the line is m and the y &#8211; intercept of the line is b.<br \/>\ny = 3x &#8211; 7<br \/>\nSlope = 3 and y &#8211; intercept = -7<\/p>\n<p>Question 2.<br \/>\ny &#8211; 1 = &#8211;\\(\\frac{2}{3}\\)x<br \/>\nAnswer:<br \/>\nWrite the equation in slope &#8211; intercept form: y = mx + b<br \/>\nThe slope of the line is m and the y &#8211; intercept of the line is b.<br \/>\ny &#8211; 1 = &#8211;\\(\\frac{2}{3}\\)x<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + 1<br \/>\nSlope = &#8211;\\(\\frac{2}{3}\\) and y &#8211; intercept = 1<\/p>\n<p><strong>Graph the linear equation. Identify the x-intercept.<\/strong><br \/>\nQuestion 3.<br \/>\ny = x &#8211; 4<br \/>\nAnswer:<br \/>\ny = x &#8211; 4<br \/>\nComparing the above equation with slope &#8211; intercept equation.<br \/>\nslope = 1, y-intercept = -4<br \/>\nPloy y &#8211; intercept and slope<br \/>\nslope = rise\/run = 1\/1<br \/>\nPlot the point that is 1 unit right and 1 unit up from (0, -4) = (1, -3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_59-300x223.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_59\" width=\"300\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_59-300x223.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_59.png 561w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThus the intercept is 4.<\/p>\n<p>Question 4.<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 1<br \/>\nAnswer:<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 1<br \/>\nComparing the above equation with slope &#8211; intercept equation.<br \/>\nSlope = &#8211;\\(\\frac{1}{2}\\), y-intercept = 1<br \/>\ny-intercept = 1. So plot (0, 1)<br \/>\nSlope = rise\/run = -1\/2<br \/>\nPlot the point that is 2 units right and 1 unit down from (0, -4) = (2, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_60-300x180.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_60\" width=\"300\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_60-300x180.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_60.png 557w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSo, the x-intercept is 2.<\/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>IN YOUR OWN WORDS<\/strong><br \/>\nConsider the graph of the equation y = mx + b.<br \/>\na. How does changing the value of m affect the graph of the equation?<\/p>\n<p>Answer:<br \/>\nThe value of m is the slope of the graph. If the value of m changes it means the slope of the graph is changing, whether it will rise or fall from left or right is dependent on the value of m.<\/p>\n<p>b. How does changing the value of b affect the graph of the equation?<br \/>\nAnswer:<br \/>\nThe value of b is the y-intercept of the graph. If the value of b changes it means it affects where the graph crosses the y &#8211; axis.<\/p>\n<p><strong>IDENTIFYING SLOPE AND y-INTERCEPT<\/strong> Find the slope and the y-intercept of the graph of the linear equation.<br \/>\nQuestion 6.<br \/>\ny = -x + 0.25<br \/>\nAnswer:<br \/>\ny = mx + c<br \/>\nslope = -1 and y &#8211; intercept = 0.25<\/p>\n<p>Question 7.<br \/>\ny &#8211; 2 = &#8211;\\(\\frac{3}{4}\\)x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny &#8211; 2 = &#8211;\\(\\frac{3}{4}\\)x<br \/>\ny = &#8211;\\(\\frac{3}{4}\\)x + 2<br \/>\nslope = &#8211;\\(\\frac{3}{4}\\) and y &#8211; intercept = 2<\/p>\n<p><strong>GRAPHING A LINEAR EQUATION<\/strong> Graph the linear equation. Identify the x-intercept.<br \/>\nQuestion 8.<br \/>\ny = x &#8211; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_61-300x261.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_61\" width=\"300\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_61-300x261.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_61.png 587w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line crosses the x-axis at (7, 0)<br \/>\nSo, the x &#8211; intercept is 7.<\/p>\n<p>Question 9.<br \/>\ny = 2x + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_62-300x275.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_62\" width=\"300\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_62-300x275.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_62.png 639w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line crosses the x &#8211; axis at (-4, 0)<br \/>\nSo, the x &#8211; intercept is -4.<\/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 10.<br \/>\nThe height y (in feet) of a movable bridge after rising for seconds is represented by the equation y = 3x + 6. Graph the equation. Interpret the y-intercept and slope. How many seconds does it take the bridge to reach a height of 76 feet? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-4.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 4\" width=\"169\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\ny = 3x + 6.<br \/>\nslope = 3, y &#8211; intercept = 16<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_63-300x289.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_63\" width=\"300\" height=\"289\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_63-300x289.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_63.png 617w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe y &#8211; intercept is 16. So, the initial height of the bridge is 16 feet.<br \/>\nThe slope is 3. So, the bridge rises 3 feet per second.<br \/>\nThe bridge will reach a height of 76 feet in 20 seconds.<\/p>\n<p>Question 11.<br \/>\nThe number of perfume bottles in storage after x months is represented by the equation y = -20x + 460. Graph the equation. Interpret the y-intercept and the slope. In how many months will there be no perfume bottles left in storage? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-5.1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 5.1\" width=\"89\" height=\"147\" \/><br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = -20x + 460<br \/>\nSlope = -20, y-intercept = 460<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_64-1-294x300.png\" alt=\"Grade 8 BIM Answers Chapter 4 img_64\" width=\"294\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_64-1-294x300.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Grade-8-BIM-Answers-Chapter-4-img_64-1.png 589w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\nThe y-intercept is 460. So, the initial number of perfume in the storage is 460.<br \/>\nThe slope is -20. So, the number of perfume bottle decrease with 20 bottles per months.<br \/>\nThere will be no perfume bottle left in the storage in 23 months.<\/p>\n<h3><a id=\"Graphing_Linear_Equations_in_Slope_Intercept_Form_Homework_&amp;_Practice_4.4\"><\/a>Graphing Linear Equations in Slope-Intercept Form Homework &amp; Practice 4.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 5\" width=\"193\" height=\"65\" \/><br \/>\nAnswer:<br \/>\n(8 &#8211; 6)\/(2 &#8211; 1) = 2\/1 = 2<br \/>\n(10 &#8211; 8)\/(3 &#8211; 2) = 2\/1 = 2<br \/>\n(12 &#8211; 10)\/(4 &#8211; 3) = 2\/1 = 2<br \/>\nThe rate of change in the table is constant.<br \/>\n(6 &#8211; y)\/(1 &#8211; 0) = 2<br \/>\n6 &#8211; y = 2<br \/>\ny = 6 &#8211; 2<br \/>\ny = 4<br \/>\nTherefore the graph does not pass through the origin.<br \/>\nSo x and y are not proportional.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-6.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 6\" width=\"189\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n(4 &#8211; 0)\/(-8 &#8211; 0) = 4\/-8 = -1\/2 = -0.5<br \/>\n(2 &#8211; 4)\/(-4 &#8211; (-8)) = -2\/4 = -1\/2 = -0.5<br \/>\n(-2 &#8211; 2)\/(4 &#8211; (-4)) = -4\/8 = -1\/2 = -0.5<br \/>\n(-4 &#8211; (-2))\/(8 &#8211; 4) = -2\/4 = -1\/2 = -0.5<br \/>\nAs the rate of change is constant, x and y are in a proportional relationship.<br \/>\ny = -0.5x<\/p>\n<p><strong>Solve the equation for y.<\/strong><br \/>\nQuestion 3.<br \/>\nx = 4y &#8211; 2<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx = 4y &#8211; 2<br \/>\nx &#8211; 2 = 4y<br \/>\ny = x\/4 + 1\/2<\/p>\n<p>Question 4.<br \/>\n3y = -6x + 1<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n3y = -6x + 1<br \/>\ny = -2x + 1\/3<\/p>\n<p>Question 5.<br \/>\n1 + y = &#8211;\\(\\frac{4}{5}\\)x &#8211; 2<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n1 + y = &#8211;\\(\\frac{4}{5}\\)x &#8211; 2<br \/>\ny = &#8211;\\(\\frac{4}{5}\\)x &#8211; 3<\/p>\n<p>Question 6.<br \/>\n2.5y = 5x &#8211; 5<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n2.5y = 5x &#8211; 5<br \/>\ny = 2x &#8211; 2<\/p>\n<p>Question 7.<br \/>\n1.3y + 5.2 = -3.9x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n1.3y + 5.2 = -3.9x<br \/>\n1.3y = -3.9x &#8211; 5.2<br \/>\ny = -3x &#8211; 4<\/p>\n<p>Question 8.<br \/>\ny &#8211; \\(\\frac{2}{3}\\)x = -6<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny &#8211; \\(\\frac{2}{3}\\)x = -6<br \/>\ny = \\(\\frac{2}{3}\\)x -6<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>GRAPHING A LINEAR EQUATION<\/strong> Graph the equation. (See Exploration 1, p. 161.)<br \/>\nQuestion 9.<br \/>\nThe graph of y = 3.5x is translated up 2 units.<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 3.5x<br \/>\nThe line obtained by translating the graph of the line y = 3.5x up 2 units has the same slope (3.5) and y &#8211; intercept 2 units greater, which means b = 0 + 2 = 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_60-300x281.png\" alt=\"Big Ideas Math Grade 8 Answer Key Chapter 4 img_60\" width=\"300\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_60-300x281.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-8-Answer-Key-Chapter-4-img_60.png 601w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 10.<br \/>\nThe graph of y = -5x is translated down 3 units.<br \/>\nAnswer:<br \/>\ny = -5x<br \/>\nThe line obtained by translating the graph of the line y = -5x down 3 units has the same slope and the y &#8211; intercept 3 units smaller, which means b = 0 &#8211; 3 = -3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_61-283x300.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_61\" width=\"283\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_61-283x300.png 283w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_61.png 553w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><\/p>\n<p><strong>MATCHING EQUATIONS AND GRAPHS<\/strong> Match the equation with its graph. Identify the slope and the y-intercept.<br \/>\nQuestion 11.<br \/>\ny = 2x + 1<br \/>\nAnswer:<br \/>\nGiven the eqation<br \/>\ny = 2x + 1<br \/>\nslope = 2 and y &#8211; intercept = 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_62-300x265.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_62\" width=\"300\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_62-300x265.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_62.png 509w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\ny = \\(\\frac{1}{3}\\)x &#8211; 2<br \/>\nAnswer:<br \/>\nslope = 1\/3 and y &#8211; intercept = -2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_63-300x247.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_63\" width=\"300\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_63-300x247.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_63.png 499w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\ny = &#8211;\\(\\frac{2}{3}\\)x + 1<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 7\" width=\"542\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-7.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-7-300x79.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Answer:<br \/>\nSlope = -2\/3 and y &#8211; intercept = 1<br \/>\nThe graph which passes through the point (0, 1) and has a negative slope is the matching graph of the given equation.<\/p>\n<p><strong>IDENTIFYING SLOPES AND y-INTERCEPTS<\/strong> Find the slope and the y-intercept of the graph of the linear equation.<br \/>\nQuestion 14.<br \/>\ny = 4x &#8211; 5<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nslope = 4 and y &#8212; intercept = -5<\/p>\n<p>Question 15.<br \/>\ny = -7x + 12<br \/>\nAnswer:<br \/>\ny = -7x + 12<br \/>\ny = mx + b<br \/>\nslpoe = -7 and y &#8211; intercept = 12<\/p>\n<p>Question 16.<br \/>\ny = &#8211;\\(\\frac{4}{5}\\)x &#8211; 2<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nslope = -4\/5<br \/>\ny &#8211; intercept = -2<\/p>\n<p>Question 17.<br \/>\ny = 2.25x + 3<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nslope = 2.25 and y &#8211; intercept = 3<\/p>\n<p>Question 18.<br \/>\ny + 1 = \\(\\frac{4}{3}\\)x<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny + 1 = \\(\\frac{4}{3}\\)x<br \/>\ny = \\(\\frac{4}{3}\\)x &#8211; 1<br \/>\nslope = \\(\\frac{4}{3}\\), y &#8211; intercept = -1<\/p>\n<p>Question 19.<br \/>\ny &#8211; 6 = \\(\\frac{3}{5}\\)x<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny &#8211; 6 = \\(\\frac{3}{5}\\)x<br \/>\ny = \\(\\frac{3}{5}\\)x + 6<br \/>\nslope = 3\/8 and y &#8211; intercept = 6<\/p>\n<p>Question 20.<br \/>\ny &#8211; 3.5 = -2x<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny &#8211; 3.5 = -2x<br \/>\ny = -2x + 3.5<br \/>\nslope = -2 and y &#8211; intercept = 3.5<\/p>\n<p>Question 21.<br \/>\ny = -5 &#8211; \\(\\frac{1}{2}\\)x<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny = -5 &#8211; \\(\\frac{1}{2}\\)x<br \/>\ny =- \\(\\frac{1}{2}\\)x &#8211; 5<br \/>\nslope = &#8211; \\(\\frac{1}{2}\\) and y &#8211; intercept = -5<\/p>\n<p>Question 22.<br \/>\ny = 11 + 1.5x<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny = 1.5x + 11<br \/>\nslope = 1.5 and y &#8211; intercept = 11<\/p>\n<p>Question 23.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the slope and y-intercept of the graph of the equation y = 4x &#8211; 3. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 8\" width=\"196\" height=\"88\" \/><br \/>\nAnswer:<br \/>\ny = 4x &#8211; 3<br \/>\nNo my friend is not correct because the y &#8211; intercept is -3.<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe number y of seasonal allergy shots available at a facility x days after receiving a shipment is represented by y = -15x + 375.<br \/>\na. Graph the linear equation.<br \/>\nb. Interpret the slope and the y-intercept.<br \/>\nAnswer:<br \/>\ny = -15x + 375<br \/>\nx = 0<br \/>\ny = -15(0) + 375 = 375<br \/>\ny = 0<br \/>\n0 = -15x + 375<br \/>\n15x = 375<br \/>\nx = 375\/15<br \/>\nx = 25<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_64-300x293.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_64\" width=\"300\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_64-300x293.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_64.png 595w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe slope shows that the number of seasonal allergy shots decrease by 15 shots each day.<br \/>\nThe y &#8211; intercept shows that the number of shots immediately after receiving a shipment is 375.<\/p>\n<p><strong>GRAPHING AN EQUATION<\/strong> Graph the linear equation. Identify the x-intercept.<br \/>\nQuestion 25.<br \/>\ny = x + 3<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = x + 3<br \/>\nslope = 1 and y &#8211; intercept = 3<br \/>\nSlope = rise\/run = 1\/1<br \/>\nPlot the point that is 1 unit right and 1 unit up from (0, 3) = (1, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_65-300x275.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_65\" width=\"300\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_65-300x275.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_65.png 527w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSo, the x &#8211; intercept is -3.<\/p>\n<p>Question 26.<br \/>\ny = 4x &#8211; 8<br \/>\nAnswer:<br \/>\ny = 4x &#8211; 8<br \/>\nComparing the above equation with slope &#8211; intercept equation.<br \/>\nslope = 4 and y &#8211; intercept = -8<br \/>\nSlope = rise\/run = 4\/1 = 4<br \/>\nPlot the point that is 1 unit right and 4 unit up from (0, -8) = (1, -4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_66-283x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_66\" width=\"283\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_66-283x300.png 283w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_66.png 531w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><\/p>\n<p>Question 27.<br \/>\ny = -3x + 9<br \/>\nAnswer:<br \/>\ny = -3x + 9<br \/>\nslope = -3 and y &#8211; intercept = 9<br \/>\nslope rise\/run = -3\/1 = -3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_67-273x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_67\" width=\"273\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_67-273x300.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_67.png 541w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><\/p>\n<p>So, the intercept is 3.<\/p>\n<p>Question 28.<br \/>\ny = -5x &#8211; 5<br \/>\nAnswer:<br \/>\ny = -5x &#8211; 5<br \/>\nslope = -5 and y &#8211; intercept = -5<br \/>\nslope = rise\/run = -5\/1<br \/>\nPlot the point that is 1 unit right and 5 unit up from (0, -5) = (1, -10)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_68-282x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_68\" width=\"282\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_68-282x300.png 282w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_68.png 571w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><br \/>\nSo, the x &#8211; intercept is -1.<\/p>\n<p>Question 29.<br \/>\ny + 14 = -7x<br \/>\nAnswer:<br \/>\ny + 14 = -7x<br \/>\ny = -7x &#8211; 14<br \/>\nslope = -7 and y &#8211; intercept = -14<br \/>\nSlope = rise\/run = -7\/1<br \/>\nPlot the point that is 1 unit right and 7 unit down from (0, -14) = (1, -21)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_69-300x296.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_69\" width=\"300\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_69-300x296.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_69.png 471w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSo, the x &#8211; intercept is -2.<\/p>\n<p>Question 30.<br \/>\ny = 8 &#8211; 2x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 8 &#8211; 2x<br \/>\ny = -2x + 8<br \/>\nslope = -2 and y &#8211; intercept = 8<br \/>\nslope = rise\/run = -2\/1<br \/>\nPlot the point 1 unit right and 2 units down from (0, 8) = (1, 6)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_70-273x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_70\" width=\"273\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_70-273x300.png 273w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_70.png 505w\" sizes=\"(max-width: 273px) 100vw, 273px\" \/><br \/>\nSo, the x &#8211; intercept is 4.<\/p>\n<p>Question 31.<br \/>\n<strong>PRECISION<\/strong><br \/>\nYou go to a harvest festival and pick apples.<br \/>\na. Which equation represents the cost (in dollars) of going to the festival and picking x pounds of apples? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 9\" width=\"555\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-9.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-9-300x103.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><br \/>\nb. Graph the equation you chose in part(a).<br \/>\nAnswer:<br \/>\nPicking a pound of apples costs $0.75, therefore x pounds cost 0.75 \u00d7 x = 0.75x<br \/>\ny = 0.75x + 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_71-260x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_71\" width=\"260\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_71-260x300.png 260w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_71.png 514w\" sizes=\"(max-width: 260px) 100vw, 260px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nWithout graphing, identify the equations of the lines that are parallel. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 10\" width=\"522\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-10.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-10-300x32.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><br \/>\nAnswer:<br \/>\nThe lines which area parallel are those having the same slope.<br \/>\ny = 2x + 4<br \/>\ny = 2x &#8211; 3<br \/>\ny = 2x + 1<br \/>\ny = 1\/2x + 1<br \/>\ny = 1\/2x + 2<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA skydiver parachutes to the ground. The height y (in feet) of the skydiver after x seconds is y = -10x + 3000.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation 4.4 11\" width=\"322\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-11.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-4.4-11-289x300.png 289w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\na. Graph the linear equation.<br \/>\nb. Interpret the slope, y-intercept, and x-intercept.<br \/>\nAnswer:<br \/>\ny = -10x + 3000<br \/>\nx = 0<br \/>\ny = -10(0) + 3000 = 3000<br \/>\ny = 0<br \/>\n0 = -10 + 3000<br \/>\n10x = 3000<br \/>\nx = 3000\/10 = 300<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_72-300x293.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_72\" width=\"300\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_72-300x293.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_72.png 584w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. The slope shows that each second the skydiver descends 10 feet.<br \/>\nThe y &#8211; intercept shows that the skydiver begins its dive from 3000 feet.<br \/>\nThe x &#8211; intercept shows that he reaches the ground after 300 seconds.<\/p>\n<p>Question 34.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nSix friends create a website. The website earns money by selling banner ads. It costs $120 a month to operate the website.<br \/>\na. A banner ad earns $0.005 per click. Write a linear equation that represents the monthly profit after paying operating costs.<br \/>\nb. Graph the equation in part(a). On the graph, label the number of clicks needed for the friends to start making a profit. Explain.<br \/>\nAnswer:<br \/>\ny = 0.005x &#8211; 120<br \/>\nx = 0<br \/>\ny = 0.005(0) &#8211; 120<br \/>\ny = -120<br \/>\ny = 0<br \/>\n0 = 0.005x &#8211; 120<br \/>\n0.005x = 120<br \/>\nx = 24000<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_73-295x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_73\" width=\"295\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_73-295x300.png 295w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_73.png 696w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><br \/>\nx &gt; 24,000<\/p>\n<h3><a id=\"Lesson_4.5_Graphing_Linear_Equations_in_Standard_Form\"><\/a>Lesson 4.5 Graphing Linear Equations in Standard Form<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Intercepts<br \/>\nWork with a partner. You spend $150 on fruit trays and vegetable trays for a party.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 1\" width=\"458\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-1.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-1-300x103.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\na. You buy x fruit trays and y vegetable trays. Complete the verbal model. Then use the verbal model to write an equation that relates x and y.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 2\" width=\"487\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-2.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-2-300x48.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nb. What is the greatest number of fruit trays that you can buy? vegetable trays? Can you use these numbers to graph your equation from part (a) in the coordinate plane? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 3\" width=\"372\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-3.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-3-300x227.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nc.Use a graph to determine the different combinations of fruit trays and vegetable trays that you can buy. Justify your answers algebraically.<br \/>\nd. You are given an extra $50 to spend. How does this affect the intercepts of your graph in part(c)? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 4\" width=\"180\" height=\"69\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 1.<br \/>\nx + y = -2<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = mx + b<br \/>\nx + y = -2<br \/>\ny = -x &#8211; 2<br \/>\nComparing the value of b and m from y = mx + b<br \/>\nm = -1 and b = -2<br \/>\nPlot y &#8211; intercept = (0, b) = (0, -2)<br \/>\nSlope = -1<br \/>\nrun\/rise = -1\/1<br \/>\nPlot the point 1 unit down and 1 unit to the right = (1, -3)<br \/>\nNow plot the points and draw the graph<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_74-300x227.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_74\" width=\"300\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_74-300x227.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_74.png 516w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + 2y = 6<br \/>\nAnswer:<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + 2y = 6<br \/>\n2y = 6 + \\(\\frac{1}{2}\\)x<br \/>\ny = 0.25x + 3<br \/>\nComparing the value of b and m from y = mx + b<br \/>\nm = 0.25 and b = 3<br \/>\nPlot y &#8211; intercept = (0, b) = (0, 3)<br \/>\nSlope = 0.25<br \/>\nrun\/rise = 0.25\/1<br \/>\nPlot the point 0.25 unit up and 1 unit to the right = (1, 3.25)<br \/>\nNow plot the points and draw the graph<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-78635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_75-296x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_75\" width=\"296\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_75-296x300.png 296w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_75.png 421w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/p>\n<p>Question 3.<br \/>\n&#8211;\\(\\frac{2}{3}\\)x + y = 0<br \/>\nAnswer:<br \/>\n&#8211;\\(\\frac{2}{3}\\)x + y = 0<br \/>\ny = \\(\\frac{2}{3}\\)x<br \/>\nComparing the value of b and m from y = mx + b<br \/>\nm = \\(\\frac{2}{3}\\) and b = 0<br \/>\nPlot y &#8211; intercept = (0, b) = (0, 0)<br \/>\nSlope =\\(\\frac{2}{3}\\)<br \/>\nrun\/rise = \\(\\frac{2}{3}\\)<br \/>\nPlot the point 0.25 unit up and 1 unit to the right = (3, 2)<br \/>\nNow plot the points and draw the graph<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_76-300x250.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_76\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_76-300x250.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_76.png 421w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\n2x + y = 5<br \/>\nAnswer:<br \/>\n2x + y = 5<br \/>\ny = -2x + 5<br \/>\nComparing the value of b and m from y = mx + b<br \/>\nm = -2 and b = 5<br \/>\nPlot y &#8211; intercept = (0, b) = (0, 5)<br \/>\nSlope = -2<br \/>\nrun\/rise = \\(\\frac{-2}{1}\\)<br \/>\nPlot the point 0.25 unit up and 1 unit to the right = (1, 3)<br \/>\nNow plot the points and draw the graph<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_77-300x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_77\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_77-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_77-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_77.png 451w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Graph the linear equation using intercepts.<\/strong><br \/>\nQuestion 5.<br \/>\n2x &#8211; y = 8<br \/>\nAnswer:<br \/>\ny = 0<br \/>\n2x &#8211; y = 8<br \/>\n2x &#8211; 0 = 8<br \/>\n2x = 8<br \/>\nx = 4<br \/>\nThe x &#8211; intercept is (4, 0)<br \/>\nY &#8211; intercept :<br \/>\nx = 0<br \/>\n2x &#8211; y = 8<br \/>\n2(0) &#8211; y = 8<br \/>\ny = -8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_78-300x275.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_78\" width=\"300\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_78-300x275.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_78.png 459w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 6.<br \/>\nx + 3y = 6<br \/>\nAnswer:<br \/>\nX-intercept:<br \/>\ny = 0<br \/>\nx + 3y = 6<br \/>\nx + 3(0) = 6<br \/>\nx + 0 = 6<br \/>\nx = 6<br \/>\nThe x &#8211; intercept is (6, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\nx + 3y = 6<br \/>\n0 + 3y = 6<br \/>\ny = 2<br \/>\nThe y &#8211; intercept is (0, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_79-300x187.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_79\" width=\"300\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_79-300x187.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_79.png 653w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/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>STRUCTURE<\/strong> Determine whether the equation is in standard form. If not, rewrite the equation in standard form.<br \/>\nQuestion 7.<br \/>\ny = x &#8211; 6<br \/>\nAnswer:<br \/>\ny = x &#8211; 6<br \/>\nThe standard form of equation is: Ax + By = C<br \/>\nThe given equation is not in the standard form.<br \/>\ny = x &#8211; 6<br \/>\nx &#8211; y = 6<\/p>\n<p>Question 8.<br \/>\ny &#8211; \\(\\frac{1}{6}\\)x + 5 = 0<br \/>\nAnswer:<br \/>\nThe standard form of equation is: Ax + By = C<br \/>\nThe given equation is not in the standard form.<br \/>\ny &#8211; \\(\\frac{1}{6}\\)x + 5 = 0<br \/>\n\\(\\frac{1}{6}\\)x &#8211; y = 5<\/p>\n<p>Question 9.<br \/>\n4x + y = 5<br \/>\nAnswer:<br \/>\nThe standard form of equation is: Ax + By = C<br \/>\nThe given equation is in the form of the standard form.<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe two ways to graph the equation 4x + 2y = 6.<br \/>\nAnswer:<br \/>\nThe two ways to graph the equation:<br \/>\n1. Graph the equation using standard form<br \/>\n2. Graph the equation using intercept.<\/p>\n<p><strong>GRAPHING A LINEAR EQUATION<\/strong> Graph the linear equation.<br \/>\nQuestion 11.<br \/>\n4x + y = 5<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n4x + y = 5<br \/>\ny = -4x + 5<br \/>\nComparing the value of b and m from y = mx + b<br \/>\nm = -4 and b = 5<br \/>\nPlot y &#8211; intercept = (0, b) = (0, 5)<br \/>\nSlope = -4<br \/>\nrun\/rise = \\(\\frac{-4}{1}\\)<br \/>\nPlot the point 4 unit down and 1 unit to the right = (1, 1)<br \/>\nNow plot the points and draw the graph<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_81-287x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_81\" width=\"287\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_81-287x300.png 287w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_81.png 483w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{1}{3}\\)x + 2y = 8<br \/>\nAnswer:<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n\\(\\frac{1}{3}\\)x + 2y = 8<br \/>\n\\(\\frac{1}{3}\\)x + 2(0) = 8<br \/>\n\\(\\frac{1}{3}\\)x = 8<br \/>\nx = 24<br \/>\nThe x &#8211; intercept is (24, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n\\(\\frac{1}{3}\\)x + 2y = 8<br \/>\n\\(\\frac{1}{3}\\)(0) + 2y = 8<br \/>\n2y = 8<br \/>\ny = 4<br \/>\nThe y &#8211; intercept is (0, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_82-300x176.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_82\" width=\"300\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_82-300x176.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_82.png 563w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\n5x &#8211; y = 10<br \/>\nAnswer:<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n5x &#8211; 0 = 10<br \/>\n5x = 10<br \/>\nx = 2<br \/>\nThe x-intercept is (2, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n5x &#8211; y = 10<br \/>\n5(0) &#8211; y = 10<br \/>\n-y = 10<br \/>\ny = -10<br \/>\nThe y &#8211; intercept is (0, -10)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_83-266x300.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_83\" width=\"266\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_83-266x300.png 266w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_83.png 391w\" sizes=\"(max-width: 266px) 100vw, 266px\" \/><\/p>\n<p>Question 14.<br \/>\nx &#8211; 3y = 9<br \/>\nAnswer:<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\nx &#8211; 3(0) = 9<br \/>\nx = 9<br \/>\nThe x &#8211; intercept is (9, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n0 &#8211; 3y = 9<br \/>\n-3y = 9<br \/>\ny = -3<br \/>\nThe y &#8211; intercept is (0, -3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_84-300x195.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_84\" width=\"300\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_84-300x195.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_84.png 657w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/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 15.<br \/>\nYou have $30 to spend on paint and clay. The equation 2x + 6y = 30 represents this situation, where x is the number of paint bottles and y is the number of tubs of clay. Graph the equation. Interpret the intercepts. How many bottles of paint can you buy if you buy 3 tubs of clay? Justify your answer.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou have $30 to spend on paint and clay.<br \/>\nThe equation 2x + 6y = 30 represents this situation,<br \/>\nwhere x is the number of paint bottles and y is the number of tubs of clay.<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n2x + 6y = 30<br \/>\n2x + 6(0) = 30<br \/>\n2x = 30<br \/>\nx = 15<br \/>\nThe x &#8211; intercept is (15, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n2x + 6y = 30<br \/>\n2(0) + 6y = 30<br \/>\n6y = 30<br \/>\ny = 5<br \/>\nThe y &#8211; intercept is (0, 5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_85-300x128.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_85\" width=\"300\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_85-300x128.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_85-768x328.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_85.png 849w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFrom the graph, I can buy 6 bottles of point if I buy 3 tubs of clay.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_86-300x120.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_86\" width=\"300\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_86-300x120.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_86-768x307.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_86.png 843w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 16.<br \/>\nYou complete two projects for a class in 60 minutes. The equation x + y = 60 represents this situation, where x is the time (in minutes) you spend assembling a birdhouse and y is the time (in minutes) you spend writing a paper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 5\" width=\"160\" height=\"145\" \/><br \/>\na. Graph the equation. Interpret the intercepts.<\/p>\n<p>Answer:<br \/>\nx + y = 60<br \/>\ny = -x + 60<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_87-300x277.png\" alt=\"BIM Grade 8 Solution Key Chapter 4 img_87\" width=\"300\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_87-300x277.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_87-768x710.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-Key-Chapter-4-img_87.png 801w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>b. You spend twice as much time assembling the birdhouse as you do writing the paper. How much time do you spend writing the paper? Justify your answer.<br \/>\nAnswer:<br \/>\nWe are given,<br \/>\ny = 2x<br \/>\n2x = -x + 60<br \/>\n2x + x = 60<br \/>\n3x = 60<br \/>\nx = 20<br \/>\ny = 2 (20)<br \/>\ny = 40<\/p>\n<h3><a id=\"Graphing_Linear_Equations_in_Standard_Form_Homework_&amp;_Practice_4.5\"><\/a>Graphing Linear Equations in Standard Form Homework &amp; Practice 4.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the slope and the y-intercept of the graph of the linear equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny = x &#8211; 1<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nSlope = -1 and y &#8211; intercept = -1<\/p>\n<p>Question 2.<br \/>\ny = -2x + 1<br \/>\nAnswer:<br \/>\ny = -2x + 1<br \/>\ny = mx + b<br \/>\nSlope = -2 and y &#8211; intercept = 1<\/p>\n<p>Question 3.<br \/>\ny = \\(\\frac{8}{9}\\)x &#8211; 8<br \/>\nAnswer:<br \/>\ny = \\(\\frac{8}{9}\\)x &#8211; 8<br \/>\ny = mx + b<br \/>\nSlope = \\(\\frac{8}{9}\\) and y &#8211; intercept = -8<\/p>\n<p><strong>Tell whether the blue figure is a reflection of the red figure.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 6\" width=\"115\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nThe blue figure is not a reflection of the red figure because, for example the reflection of the upper leg of the upper leg of the red triangle across the y-axis is the top vertex of the blue triangle, not a point.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 7\" width=\"144\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nThe blue figure is a reflection of the red figure because to each point in the red figure corresponds a symmetrical point in the blue figure.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 8\" width=\"133\" height=\"132\" \/><br \/>\nAnswer:<br \/>\nThe blue figure is a reflection of the red figure because to each point in the red figure corresponds a symmetrical point in the blue figure.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>USING INTERCEPTS<\/strong> Define two variables for the verbal model. Write an equation in slope-intercept form that relates the variables. Graph the equation using intercepts. (See Exploration 1, p. 167.)<br \/>\nQuestion 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 9\" width=\"383\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-9.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-9-300x41.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\nAnswer:<br \/>\nx = amount of peaches (in pounds)<br \/>\ny = the amount of apples (in pounds)<br \/>\n2x + 1.5y = 15<br \/>\ny = 0 = 2x + 1.5(0) = 15<br \/>\n2x = 15<br \/>\nx = 7.5<br \/>\nx = 0<br \/>\n2(0) + 1.5y = 15<br \/>\n1.5y =15<br \/>\ny = 10<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_88-250x300.png\" alt=\"BIM Grade 8 Solution key Chapter 4 img_88\" width=\"250\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_88-250x300.png 250w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_88.png 619w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 10\" width=\"388\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-10.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-10-300x42.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nAnswer:<br \/>\nx = the biked distance (in miles)<br \/>\ny = the walked distance (in miles)<br \/>\ny = 0<br \/>\n16x + 2(0) = 32<br \/>\n16x = 32<br \/>\nx = 2<br \/>\nx = 0<br \/>\n16(0) + 2y = 32<br \/>\n2y = 32<br \/>\ny = 16<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_89-251x300.png\" alt=\"BIM Grade 8 Solution key Chapter 4 img_89\" width=\"251\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_89-251x300.png 251w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solution-key-Chapter-4-img_89.png 621w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p><strong>REWRITING AN EQUATION<\/strong> Write the linear equation in slope-intercept form.<br \/>\nQuestion 9.<br \/>\n2x + y = 17<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n2x + y = 17<br \/>\ny = 17 &#8211; 2x<br \/>\ny = -2x + 17<\/p>\n<p>Question 10.<br \/>\n5x &#8211; y = \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n5x &#8211; y = \\(\\frac{1}{4}\\)<br \/>\n-y = \\(\\frac{1}{4}\\) &#8211; 5x<br \/>\ny = 5x &#8211; \\(\\frac{1}{4}\\)<\/p>\n<p>Question 11.<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + y = 10<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + y = 10<br \/>\ny = \\(\\frac{1}{2}\\)x + 10<\/p>\n<p><strong>GRAPHING AN EQUATION<\/strong> Graph the linear equation.<br \/>\nQuestion 12.<br \/>\n-18x + 9y = 72<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n-18x + 9y = 72<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n-18x + 9(0) = 72<br \/>\n-18x = 72<br \/>\nx = -4<br \/>\nThe x &#8211; intercept is (-4, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n-18x + 9y = 72<br \/>\n-18(0) + 9y = 72<br \/>\n9y = 72<br \/>\ny = 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_90-285x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_90\" width=\"285\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_90-285x300.png 285w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_90.png 509w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/><\/p>\n<p>Question 13.<br \/>\n16x &#8211; 4y = 2<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n16x &#8211; 4y = 2<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n16x &#8211; 4y = 2<br \/>\n16x &#8211; 4(0) = 2<br \/>\n16x = 2<br \/>\nx = 0.125<br \/>\nThe X &#8211; intercept is (0.125, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n16(0) &#8211; 4y = 2<br \/>\n-4y = 2<br \/>\ny = -2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_91-210x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_91\" width=\"210\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_91-210x300.png 210w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_91.png 403w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{1}{4}\\)x + \\(\\frac{3}{4}\\)y = 1<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n\\(\\frac{1}{4}\\)x + \\(\\frac{3}{4}\\)y = 1<br \/>\nx + 3y = 4<br \/>\ny = 0<br \/>\nx + 3(0) = 4<br \/>\nx = 4<br \/>\nx = 0<br \/>\n0 + 3y = 4<br \/>\n3y = 4<br \/>\ny = 4\/3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_93-300x189.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_93\" width=\"300\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_93-300x189.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_93-768x483.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_93.png 946w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>MATCHING<\/strong> Match the equation with its graph.<br \/>\nQuestion 15.<br \/>\n15x &#8211; 12y = 60<br \/>\nAnswer:<br \/>\ny = 0<br \/>\n15x &#8211; 12(0) = 60<br \/>\n15x = 60<br \/>\nx = 60\/15<br \/>\nx = 4<br \/>\nx = 0<br \/>\n15(0) &#8211; 12y = 60<br \/>\n-12y = 60<br \/>\ny = -5<br \/>\nThe graph having the x &#8211; intercept 4 and y &#8211; intercept -5<\/p>\n<p>Question 16.<br \/>\n5x + 4y = 20<br \/>\nAnswer:<br \/>\nGiven the linear equation<br \/>\n5x + 4y = 20<br \/>\ny = 0<br \/>\n5x + 4(0) = 20<br \/>\n5x = 20<br \/>\nx = 4<br \/>\nx = 0<br \/>\n5(0) + 4y = 20<br \/>\n4y = 20<br \/>\ny = 5<\/p>\n<p>Question 17.<br \/>\n10x + 8y = -40<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-11.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 11\" width=\"533\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-11.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-11-300x81.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\n10x + 8y = -40<br \/>\ny = 0<br \/>\n10x + 8(0) = -40<br \/>\n10x = -40<br \/>\nx = -4<br \/>\nx = 0<br \/>\n10(0) + 8y = -40<br \/>\n8y = -40<br \/>\ny = -5<\/p>\n<p>Question 18<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the x-intercept of -2x + 3y = 12. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-12.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 12\" width=\"179\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n-2x + 3y = 12<br \/>\ny = 0<br \/>\n-2x + 3(0) = 12<br \/>\n-2x = 12<br \/>\nx = -6<br \/>\nYour friend is not correct because the x &#8211; intercept is the value of x corresponding to y = 0.<br \/>\nYour friend computed the y &#8211; intercept.<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA charm bracelet costs $65, plus $25 for each charm. The equation -25x + y = 65 represents the cost y (in dollars) of the bracelet, where x is the number of charms.<br \/>\na. Graph the equation.<br \/>\nb. How much does a bracelet with three charms cost?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_94-300x211.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_94\" width=\"300\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_94-300x211.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_94-768x540.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_94.png 868w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny = 25x + 65<br \/>\nSubstitute the value of x in the equation<br \/>\ny = 25(3) + 65<br \/>\ny = 75 + 65<br \/>\ny = 140<\/p>\n<p><strong>USING INTERCEPTS TO GRAPH<\/strong> Graph the linear equation using intercepts.<br \/>\nQuestion 20.<br \/>\n3x &#8211; 4y = -12<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n3x &#8211; 4y = -12<br \/>\n3x &#8211; 4(0) = -12<br \/>\n3x = -12<br \/>\nx = -4<br \/>\nThe x &#8211; intercept is (-4, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n3(0) &#8211; 4y = -12<br \/>\n-4y = -12<br \/>\ny = 3<br \/>\nThe y &#8211; intercept is (0, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_95-300x204.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_95\" width=\"300\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_95-300x204.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_95.png 593w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 21.<br \/>\n2x + y = 8<br \/>\nAnswer:<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n2x + y = 8<br \/>\n2x + 0 = 8<br \/>\n2x = 8<br \/>\nx = 4<br \/>\nThe x &#8211; intercept is (4, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n2x + y = 8<br \/>\n2(0) + y = 8<br \/>\ny = 8<br \/>\nThe y &#8211; intercept is (0, 8)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_96-291x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_96\" width=\"291\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_96-291x300.png 291w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_96.png 517w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{1}{3}\\)x &#8211; \\(\\frac{1}{6}\\)y = &#8211;\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\nX &#8211; intercept:<br \/>\ny = 0<br \/>\n\\(\\frac{1}{3}\\)x &#8211; \\(\\frac{1}{6}\\)(0) = &#8211;\\(\\frac{2}{3}\\)<br \/>\n\\(\\frac{1}{3}\\)x = &#8211;\\(\\frac{2}{3}\\)<br \/>\nx = -2<br \/>\nThe x &#8211; intercept is (-2, 0)<br \/>\nY &#8211; intercept:<br \/>\nx = 0<br \/>\n\\(\\frac{1}{3}\\)(0) &#8211; \\(\\frac{1}{6}\\)y = &#8211;\\(\\frac{2}{3}\\)<br \/>\ny = 4<br \/>\nThe y &#8211; intercept is (0, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_97-267x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_97\" width=\"267\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_97-267x300.png 267w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_97.png 421w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYour cousin has $90 to spend on video games and movies. The equation 30x + 15y = 90 represents this situation, where x is the number of video games purchased and y is the number of movies purchased. Graph the equation. Interpret the intercepts.<br \/>\nAnswer:<br \/>\n30x + 15y = 90<br \/>\nx = 0<br \/>\n30(0) + 15y = 90<br \/>\n15y = 90<br \/>\ny = 6<br \/>\ny = 0<br \/>\n30x + 15(0) = 90<br \/>\n30x = 90<br \/>\nx = 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_98-300x245.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_98\" width=\"300\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_98-300x245.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_98-768x626.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_98.png 887w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe x &#8211; intercept shows that 3 video games are purchased when no movies are purchased.<br \/>\nThe y &#8211; intercept shows that 6 movies are purchased when no video games are purchased.<\/p>\n<p>Question 24.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA group of friends go scuba diving. They rent a boat for x days and scuba gear for y people, represented by the equation 250x + 50y = 1000.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-13.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 13\" width=\"274\" height=\"156\" \/><br \/>\na. Graph the equation and interpret the intercepts.<br \/>\nb. How many friends can go scuba diving if they rent the boat for 1 day? 2 days?<br \/>\nc. How much money is spent in total?<br \/>\nAnswer:<br \/>\n250x + 50y = 1000<br \/>\nx = 0<br \/>\n250(0) + 50y = 1000<br \/>\n50y = 1000<br \/>\ny = 20<br \/>\nwhen y = 0<br \/>\n250x + 50(0) = 1000<br \/>\n250x = 1000<br \/>\nx = 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_99-225x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_99\" width=\"225\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_99-225x300.png 225w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_99.png 481w\" sizes=\"(max-width: 225px) 100vw, 225px\" \/><br \/>\nb.<br \/>\n250(1) + 50y = 1000<br \/>\n250 + 50y = 1000<br \/>\n50y = 1000 &#8211; 250<br \/>\n50y = 750<br \/>\ny = 15<br \/>\nwhen x = 2<br \/>\n250(2) + 50y = 1000<br \/>\n500 + 50y = 1000<br \/>\n50y = 1000 &#8211; 500<br \/>\n50y = 500<br \/>\ny = 500\/50<br \/>\ny = 10<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou work at a restaurant as a host and a server. You earn $9.45 for each hour you work as a host and $3.78 for each hour you work as a server.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-14.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 14\" width=\"164\" height=\"145\" \/><br \/>\na. Write an equation in standard form that models your earnings.<br \/>\nb. Graph the equation.<br \/>\nAnswer:<br \/>\nYou earn $9.45 for each hour you work as a host and $3.78 for each hour you work as a server.<br \/>\nNumber of hours worked as host + $3.78.<br \/>\nNumber of hours worked as server = $113.40<br \/>\n9.45x + 3.78y = 113.40<br \/>\nx = 0<br \/>\n9.45(0) + 3.78y = 113.40<br \/>\n3.78y = 113.40<br \/>\ny = 30<br \/>\nwhen y = 0<br \/>\n9.45x + 3.78(0) = 113.40<br \/>\n9.45x = 113.40<br \/>\nx = 12<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_100-300x253.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_100\" width=\"300\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_100-300x253.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_100.png 723w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>LOGIC<\/strong><br \/>\nDoes the graph of every linear equation have an x-intercept? Justify your reasoning.<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\ny = 0<br \/>\n0 = mx + b<br \/>\nmx = -b<br \/>\nx = -b\/m for m \u2260 0<br \/>\nIf m = 0 the equation has no solution. Therefore the equation y = b has no x &#8211; intercept.<\/p>\n<p>Question 27.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nFor a house call, a veterinarian charges $70, plus $40 per hour.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.5-15.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.5 15\" width=\"164\" height=\"252\" \/><br \/>\na. Write an equation that represents the total fee y (in dollars) the veterinarian charges for a visit lasting x hours.<\/p>\n<p>b. Find the x-intercept. Does this value make sense in this context? Explain your reasoning.<br \/>\nc. Graph the equation.<br \/>\nAnswer:<br \/>\nTotal fee = fixed charge + number of hours . cost per hour<br \/>\ny = 70 + 40x<br \/>\ny = 0<br \/>\n0 = 70 + 40x<br \/>\n-70 = 40x<br \/>\nx = -1.75<br \/>\nx = 0<br \/>\ny = 70 + 40(0)<br \/>\ny = 70<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solutions-Chapter-4-img_101-300x300.png\" alt=\"BIM Grade 8 Solutions Chapter 4 img_101\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solutions-Chapter-4-img_101-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solutions-Chapter-4-img_101-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solutions-Chapter-4-img_101-768x765.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Solutions-Chapter-4-img_101.png 774w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><a id=\"Lesson_4.6_Writing_Equations_in_Slope_Intercept_Form\"><\/a>Lesson 4.6 Writing Equations in Slope-Intercept Form<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing Equations of Lines<br \/>\nWork with a partner.For each part, answer the following questions.<\/p>\n<ul>\n<li>What are the slopes and the y-intercepts of the lines?<\/li>\n<li>What are equations that represent the lines?<\/li>\n<li>What do the lines have in common?<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 1\" width=\"653\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-1.png 653w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-1-300x114.png 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Interpreting the Slope and the y-Intercept<br \/>\nWork with a partner. The graph represents the distance y (in miles) of a car from Phoenix after t hours of a trip.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-2.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 2\" width=\"203\" height=\"218\" \/><br \/>\na. Find the slope and the y-intercept of the line. What do they represent in this situation?<br \/>\nb. Write an equation that represents the graph.<br \/>\nc. How can you determine the distance of the car from Phoenix after 11 hours?<br \/>\nAnswer:<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write an equation in slope-intercept form of the line that passes through the given points.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-3.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 3\" width=\"154\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-3.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-3-150x150.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (4 &#8211; 2)\/(1 &#8211; 0)<br \/>\n= 2\/1<br \/>\n= 2<br \/>\nBecause the line crosses the y &#8211; axis at (0, 2)<br \/>\ny = mx + b<br \/>\ny = 2x + 2<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-4.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 4\" width=\"95\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-1 &#8211; 3)\/(0 &#8211; (-3))<br \/>\n= -4\/3<br \/>\nBecause y = -1 when x = 0, the y &#8211; intercept is -1<br \/>\ny = mx + b<br \/>\ny = -4\/3 x &#8211; 1<\/p>\n<p><strong>Write an equation of the line that passes through the given points.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-5.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 5\" width=\"137\" height=\"60\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (5 &#8211; 5)\/(0 &#8211; (-4))<br \/>\n= 0\/4<br \/>\nBecause y = 5 when x = 0, the y &#8211; intercept is 5<br \/>\ny = mx + b<br \/>\ny = (0)x + 5<br \/>\ny = 5<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-6.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 6\" width=\"151\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (1 &#8211; 1)\/(3 &#8211; 0)<br \/>\n= 0\/3<br \/>\n= 0<br \/>\nBecause the line crosses the y &#8211; axis at (0, 1) the y &#8211; intercept is 1<br \/>\ny = mx + b<br \/>\ny = (0)x + 1<br \/>\ny = 1<\/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 EQUATIONS IN SLOPE-INTERCEPT FORM<\/strong> Write an equation in slope-intercept form of the line that passes through the given points.<br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-7.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 7\" width=\"92\" height=\"150\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (5 &#8211; 2)\/(1 &#8211; 0)<br \/>\n= 3\/1<br \/>\n= 3<br \/>\nBecause y = 2 when x = 0, the y &#8211; intercept is 2<br \/>\ny = mx + b<br \/>\ny = (3)x + 2<br \/>\ny = 3x + 2<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-8.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 8\" width=\"148\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-1 &#8211; 5)\/(1 &#8211; (-1))<br \/>\n= -6\/2<br \/>\n= -3<br \/>\nBecause the line crosses the y &#8211; axis at (0, 2) the y &#8211; intercept is 2<br \/>\ny = mx + b<br \/>\ny = -3x + 2<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING AN EQUATION<\/strong><br \/>\nWrite an equation of the line that passes through (0, -5) and (2, -5).<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-5 &#8211; (-5))\/(2 &#8211; 0)<br \/>\n= 0\/2<br \/>\n= 0<br \/>\nBecause y = -5 when x = 0, the y &#8211; intercept is -5<br \/>\ny = mx + b<br \/>\ny = (0)x + -5<br \/>\ny = -5<\/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 8.<br \/>\nYou load boxes onto an empty truck at a constant rate. After 3 hours, there are 100 boxes on the truck. How much longer do you work if you load a total of 120 boxes? Justify your answer.<br \/>\nAnswer:<br \/>\nLet x be the number of hours you work if you load a total of 120 boxes.<br \/>\n100\/3 = 120\/x<br \/>\n100x = 3 \u00d7 120<br \/>\nx = 360\/100<br \/>\nx = 3.6 hours<br \/>\n3.6 &#8211; 3 = 0.6 hours<\/p>\n<p>Question 9.<br \/>\nThe table shows the amounts (in tons) of waste left in a landfill after x months of waste relocation. Interpret the slope and the y-intercept of the line that passes through the given points. How many months does it take to empty the landfill? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-9.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 9\" width=\"141\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nm = (12 &#8211; 15)\/ (6 &#8211; 0)<br \/>\nm = -3\/6<br \/>\nm = -0.5<br \/>\nb = 15<br \/>\nThe y &#8211; intercept shows that there are 150 tons of waste in the beginning.<br \/>\ny = -0.5x + 15<br \/>\ny = 0<br \/>\n0 = -0.5x + 15<br \/>\nx = 30<br \/>\nSo the ladfill will be emptied after 30 months.<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA lifetime subscription to a website costs $250. A monthly subscription to the website costs $10 to join and $15 per month. Write equations to represent the costs of each plan. If you want to be a member for one year, which plan is less expensive? Explain.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA lifetime subscription to a website costs $250. A monthly subscription to the website costs $10 to join and $15 per month.<br \/>\nTotal cost for plan 1 = the lifetime subscription<br \/>\ny = 250<br \/>\nTotal cost for Plan 2 = Fixed tax + Number of months . monthly cost<br \/>\ny = 10 + 15x<br \/>\nPlan 1: y = 250<br \/>\nPlan 2: y = 10 + 15(12) = 190<br \/>\nAs 190 &lt; 250, plan 1 is less expensive.<\/p>\n<h3><a id=\"Writing_Equations_in_Slope_Intercept_Form_Homework_&amp;_Practice_4.6\"><\/a>Writing Equations in Slope-Intercept Form Homework &amp; Practice 4.6<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the linear equation in slope-intercept form.<\/strong><br \/>\nQuestion 1.<br \/>\n4x + y = 1<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n4x + y = 1<br \/>\ny = -4x + 1<\/p>\n<p>Question 2.<br \/>\nx &#8211; y = \\(\\frac{1}{5}\\)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx &#8211; y = \\(\\frac{1}{5}\\)<br \/>\nx &#8211; \\(\\frac{1}{5}\\) = y<\/p>\n<p>Question 3.<br \/>\n&#8211;\\(\\frac{2}{3}\\)x + 2y = -7<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n&#8211;\\(\\frac{2}{3}\\)x + 2y = -7<br \/>\n2y = -7 + \\(\\frac{2}{3}\\)x<br \/>\ny = \\(\\frac{1}{3}\\)x &#8211; \\(\\frac{7}{2}\\)<\/p>\n<p><strong>Plot the ordered pair in a coordinate plane.<\/strong><br \/>\nQuestion 4.<br \/>\n(1, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_102-297x300.png\" alt=\"8th Grade BIM Answers Chapter 4 img_102\" width=\"297\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_102-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_102.png 407w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Question 5.<br \/>\n(-1, -2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_103-300x255.png\" alt=\"8th Grade BIM Answers Chapter 4 img_103\" width=\"300\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_103-300x255.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_103.png 477w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 6.<br \/>\n(0, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_104-300x269.png\" alt=\"8th Grade BIM Answers Chapter 4 img_104\" width=\"300\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_104-300x269.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_104.png 465w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\n(2, 7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_105-231x300.png\" alt=\"8th Grade BIM Answers Chapter 4 img_105\" width=\"231\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_105-231x300.png 231w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-BIM-Answers-Chapter-4-img_105.png 393w\" sizes=\"(max-width: 231px) 100vw, 231px\" \/><\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>INTERPRETING THE SLOPE AND THE y-INTERCEPT<\/strong> The graph y represents the cost (in dollars) to open an online gaming account and buy x games. (See Exploration 2, p. 173.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-10.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 10\" width=\"218\" height=\"210\" \/><br \/>\nQuestion 8.<br \/>\nFind the slope and the y-intercept of the line. What do they represent in this situation?<br \/>\nAnswer:<br \/>\n(0, 15), (3, 45)<br \/>\nm = (45 &#8211; 15)\/(3 &#8211; 0)<br \/>\nm = 30\/3 10<br \/>\nThus the slope of the line is m &#8211; 3.<br \/>\nb = 15<br \/>\nThe slope represents the cost of one game, while the y &#8211; intercept is the cost of opening the gaming account.<\/p>\n<p>Question 9.<br \/>\nWrite an equation that represents the graph.<br \/>\nAnswer:<br \/>\nm = 10<br \/>\nb = 15<br \/>\ny = mx + b<br \/>\ny = 10x + 15<\/p>\n<p>Question 10.<br \/>\nHow can you determine the total cost of opening an account and buying 6 games?<br \/>\nAnswer:<br \/>\ny = 10x + 15<br \/>\ny = 10(6) + 15<br \/>\ny = 60 + 15<br \/>\ny = 75<\/p>\n<p><strong>WRITING EQUATIONS IN SLOPE-INTERCEPT FORM<\/strong> Write an equation in slope-intercept form of the line that passes through the given points.<br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-11.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 11\" width=\"146\" height=\"142\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (4 &#8211; 3)\/(0 &#8211; (-1))<br \/>\n= 1\/1<br \/>\n= 1<br \/>\nBecause the line crosses the y &#8211; axis at (0, 4) the y &#8211; intercept is 4<br \/>\ny = mx + b<br \/>\ny = (1)x + 4<br \/>\ny = x + 4<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-12.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 12\" width=\"145\" height=\"139\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (6 &#8211; 0)\/(-3 &#8211; 0)<br \/>\n= 6\/-3<br \/>\n= -2<br \/>\nBecause the line crosses the y &#8211; axis at (0, 2) the y &#8211; intercept is 2<br \/>\ny = mx + b<br \/>\ny = -2x + 0<br \/>\ny = -2x<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-13.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 13\" width=\"142\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (2 &#8211; 1)\/(4 &#8211; 0)<br \/>\n= 1\/4<br \/>\nBecause the line crosses the y &#8211; axis at (0, 1) the y &#8211; intercept is 1<br \/>\ny = mx + b<br \/>\ny = 1\/4 x + 1<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-14.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 14\" width=\"87\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (1 &#8211; 2)\/(0 &#8211; (-2))<br \/>\n= -1\/2<br \/>\nBecause y = 1 when x = 0, the y &#8211; intercept is 1<br \/>\ny = mx + b<br \/>\ny = -1\/2 x + 2<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-15.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 15\" width=\"97\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-3 &#8211; (-4))\/(0 &#8211; (-3))<br \/>\n= 1\/3<br \/>\nBecause y = -3 when x = 0, the y &#8211; intercept is -3<br \/>\ny = mx + b<br \/>\ny = 1\/3 x &#8211; 3<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-16.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 16\" width=\"96\" height=\"153\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-1 -4)\/(0 &#8211; (-2))<br \/>\n= -5\/2<br \/>\nBecause y = -1 when x = 0, the y &#8211; intercept is -1<br \/>\ny = mx + b<br \/>\ny = -5\/2 x &#8211; 1<\/p>\n<p><strong>WRITING EQUATIONS<\/strong> Write an equation of the line that passes through the given points.<br \/>\nQuestion 17.<br \/>\n(-1, 4), (0, 2)<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (2 &#8211; 4)\/(0 &#8211; (-1))<br \/>\n= -2\/1<br \/>\n= -2<br \/>\nBecause y = 2 when x = 0, the y &#8211; intercept is 2<br \/>\ny = mx + b<br \/>\ny = -2x + 2<\/p>\n<p>Question 18.<br \/>\n(-1, 0), (0, 0)<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (0 &#8211; 0)\/(0 &#8211; (-1))<br \/>\n= 0\/1<br \/>\n= 0<br \/>\nBecause y = 0 when x = 0, the y &#8211; intercept is 0<br \/>\ny = mx + b<br \/>\ny = 0<\/p>\n<p>Question 19.<br \/>\n(0, 4), (0, -3)<br \/>\nAnswer:<br \/>\nBoth points belong to the y-axis. Therefore the equation of the line passing through them is<br \/>\nx = 0<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes an equation of the line shown. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-17.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 17\" width=\"277\" height=\"173\" \/><br \/>\nAnswer:<br \/>\nBecause in the given graph, y = -2 when x = 0, so the y &#8211; intercept is -2. The equation of the line should be: y = 1\/2 x &#8211; 2<br \/>\nNo my friend is NOT correct.<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation in slope y-intercept form that represents the length (in feet) of a boa constrictor that is x years old.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-18.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 18\" width=\"236\" height=\"167\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA boa constrictor is 18 inches long at birth and grows 8 inches per year.<br \/>\nLength after x years = birth length + number of years . Growth per year<br \/>\ny = 18 + 8x<br \/>\ny = 8x + 18<br \/>\nConvert it into feet<br \/>\ny = 2\/3 x + 3\/2<\/p>\n<p>Question 22.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the speeds y (in miles per hour) of a car after x seconds of braking. Write an equation of the line that passes through the points in the table. Interpret the slope and the y-intercept of the line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-19.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 19\" width=\"205\" height=\"76\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (60 &#8211; 70)\/(1 &#8211; 0)<br \/>\n= -10\/1<br \/>\n= -10<br \/>\nBecause y = 70 when x = 0, the y &#8211; intercept is 70<br \/>\ny = mx + b<br \/>\ny = -10x + 70<br \/>\nSlope = -10 represents the decrease in the speed of the car each seconds after breaking.<br \/>\nThe y &#8211; intercept of 70 represents the initial speed of the car.<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA dentist charges a flat fee for an office visit, plus an additional fee for every tooth removed. The graph shows the total cost y (in dollars) for a patient when the dentist removes x teeth. Interpret the slope and the y-intercept.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-20.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 20\" width=\"165\" height=\"192\" \/><br \/>\nAnswer:<br \/>\n(2, 500), (4, 900)<br \/>\nm = (900 &#8211; 500)\/(4 &#8211; 2)<br \/>\nm = 400\/2<br \/>\nm = 200<br \/>\ny = mx + b<br \/>\n500 = 200(2) + b<br \/>\n500 = 400 + b<br \/>\nb = 500 &#8211; 400<br \/>\nb = 100<br \/>\nThe slope shows that the amount charged for each removed tooth is $200.<br \/>\nThe y &#8211; intercept shows that the flat fee for an office visit is $100.<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nOne of your friends gives you $10 for a charity walkathon. Another friend gives you an amount per mile. After 5 miles, you have raised $13.50 total. Write an equation that represents the amount y of money you have raised after x miles.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nOne of your friends gives you $10 for a charity walkathon.<br \/>\nAnother friend gives you an amount per mile. After 5 miles, you have raised $13.50 total.<br \/>\ny = mx + b<br \/>\nb = 10<br \/>\n13.50 = 5m + 10<br \/>\n13.50 &#8211; 10 = 5m<br \/>\n3.50 = 5m<br \/>\nm = 3.50\/5<br \/>\nm = 0.7<br \/>\ny = 0.7x + 10<\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have 500 sheets of notebook paper. After 1 week, you have 72% of the sheets left. You use the same number of sheets each week. Write an equation that represents the number y of sheets remaining after x weeks.<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\n500 &#8211; 0.72 \u00d7 500 = 500 &#8211; 360 = 140 sheets<br \/>\nm = -140<br \/>\nb = 500<br \/>\ny = -140x + 500<\/p>\n<p>Question 26.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe palm tree on the left is 10 years old. The palm tree on the right is 8 years old. The trees grow at the same rate.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-Graphing-and-Writing-Linear-Equations-4.6-21.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 Graphing and Writing Linear Equations 4.6 21\" width=\"291\" height=\"271\" \/><br \/>\na. Estimate the height y (in feet) of each tree.<br \/>\nb. Plot the two points (x, y), where x is the age of each tree and y is the height of each tree.<br \/>\nc. What is the rate of growth of the trees?<br \/>\nd. Write an equation that represents the height of a palm tree in terms of its age.<br \/>\nAnswer:<br \/>\na. estimate<br \/>\nleft: 18<br \/>\nright: 12<br \/>\nplot y = 1.8x<\/p>\n<h3><a id=\"Lesson_4.7_Writing_Equations_in_Point_Slope_Form\"><\/a>Lesson 4.7 Writing Equations in Point-Slope Form<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Deriving an Equation<br \/>\nWork with a partner. Let (x<sub>1<\/sub>, y<sub>1<\/sub>) represent a specific point on a line. Let (x, y) represent any other point on the line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 1\" width=\"423\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-1.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-1-300x115.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><br \/>\na. Write an equation that represents the slope m of the line. Explain your reasoning.<br \/>\nb. Multiply each side of your equation in part(a) by the expression in the denominator. What does the resulting equation represent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing an Equation<br \/>\nWork with a partner.<br \/>\nFor 4 months, you saved $25 a month. You now have $175 in your savings account.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 2\" width=\"228\" height=\"250\" \/><br \/>\na. Draw a graph that shows the balance in your account after t months.<br \/>\nb.Use your result from Exploration 1 to write an equation that represents the balance A after t months.<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 3\" width=\"184\" height=\"87\" \/><\/p>\n<p><strong>Try It<\/strong><br \/>\n<strong>Write an equation in point -slope form of the line that passes through the given point and has the given slope.<\/strong><br \/>\nQuestion 1.<br \/>\n(1, 2); m = -4<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 2 = -4(x &#8211; (1))<br \/>\ny &#8211; 2 = -4(x &#8211; 1)<\/p>\n<p>Question 2.<br \/>\n(7, 0); m = 1<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 0 = 1(x &#8211; (7))<br \/>\ny &#8211; 0 = 1(x &#8211; 7)<\/p>\n<p>Question 3.<br \/>\n(-8, -5); m = &#8211;\\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-5) = &#8211;\\(\\frac{3}{4}\\)(x &#8211; (-8))<br \/>\ny + 5 = &#8211;\\(\\frac{3}{4}\\)(x + 8)<\/p>\n<p><strong>Write an equation in slope-intercept form of the line that passes through the given points.<\/strong><br \/>\nQuestion 4.<br \/>\n(-2, 1), (3, -4)<br \/>\nAnswer:<br \/>\nSlope(m) = (-4 &#8211; 1)\/(3 &#8211; (-2))<br \/>\n= -5\/5<br \/>\nm = -1<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 1 = -1(x &#8211; (-2))<br \/>\ny &#8211; 1 = -1(x + 2)<br \/>\ny &#8211; 1 = -x &#8211; 2<br \/>\ny = -x &#8211; 1<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-4.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 4\" width=\"172\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nSlope(m) = (3 &#8211; 5)\/(-3 &#8211; (-5))<br \/>\n= -2\/2<br \/>\nm = -1<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 1 = -1(x &#8211; (-1))<br \/>\ny &#8211; 1 = -1(x + 1)<br \/>\ny &#8211; 1 = -x &#8211; 1<br \/>\ny = -x &#8211; 1 + 1<br \/>\ny = -x<\/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 AN EQUATION<\/strong> Write an equation in point-slope form of the line that passes through the given point and has the given slope.<br \/>\nQuestion 6.<br \/>\n(2, 0); m = 1<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 0 = 1(x &#8211; (2))<br \/>\ny &#8211; 0 = 1(x &#8211; 2)<\/p>\n<p>Question 7.<br \/>\n(-3, -1); m = &#8211;\\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-1) = &#8211;\\(\\frac{1}{3}\\)(x &#8211; (-3))<br \/>\ny + 1 = &#8211;\\(\\frac{1}{3}\\)(x + 3)<\/p>\n<p>Question 8.<br \/>\n(5, 4); m = 3<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 4 = 3(x &#8211; (5))<br \/>\ny &#8211; 4 = 3(x &#8211; 5)<\/p>\n<p>Question 9.<br \/>\n<strong>WRITING AN EQUATION<\/strong><br \/>\nWrite an equation of the line that passes through the points given in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-5.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 5\" width=\"156\" height=\"63\" \/><br \/>\nAnswer:<br \/>\nSlope(m) = (-2 &#8211; 1)\/(5 &#8211; 3)<br \/>\n= -3\/2<br \/>\nm = -1<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-5) = -3\/2(x &#8211; 7)<br \/>\ny + 5 = -3\/2(x &#8211; 7)<br \/>\ny + 5 = -3\/2 x + 21\/2<br \/>\ny = -3\/2 x + 11\/2<\/p>\n<p>Question 10.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Sketch \u201cboth\u201d graphs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-6.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 6\" width=\"442\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-6.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-6-300x77.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><br \/>\nAnswer:<br \/>\ny &#8211; 7 = 4x &#8211; 4<br \/>\ny = 4x + -4 + 7<br \/>\ny = 4x + 3<br \/>\nGraph line passes through the points (4, 5) and (5, 9)<\/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 \/>\nA writer finishes a project that a coworker started at a rate of 3 pages per hour. After 3 hours,25% of the project is complete.<br \/>\na. The project is 200 pages long. Write and graph an equation for the total number y of pages that have been finished after the writer works for x hours.<br \/>\nb. The writer has a total of 45 hours to finish the project. Will the writer meet the deadline? Explain your reasoning.<br \/>\nAnswer:<br \/>\nm = 3<br \/>\ny = 3x + b<br \/>\nb + 9 = 25%(200)<br \/>\nb + 9 = 0.25(200)<br \/>\nb + 9 = 50<br \/>\nb = 50 &#8211; 9<br \/>\nb = 41<br \/>\ny = 3x + 41<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_106-300x107.png\" alt=\"BIM 8th Grade Solution Key Ch 4 img_106\" width=\"300\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_106-300x107.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_106-1024x365.png 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_106-768x274.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_106.png 1189w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny = 3x + 41<br \/>\ny = 3(45) + 41 = 176 pages<br \/>\nAs 176 &lt; 200, the writer will not meet the deadline.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and your friend begin to run along a path at different constant speeds.After 1 minute,your friend is 45 meters ahead of you. After 3 minutes, your friend is 105 meters ahead of you.<br \/>\na. Write and graph an equation for the distance y (in meters) your friend is ahead of you after x minutes. Justify your answer.<\/p>\n<p>Answer:<br \/>\ny = mx + b<br \/>\n45 = m + b<br \/>\n105 = 3m + b<br \/>\n105 &#8211; 45 = (3m + b) &#8211; (m + b)<br \/>\n60 = 2m<br \/>\nm = 30<br \/>\n45 = 30 + b<br \/>\nb = 45 &#8211; 30<br \/>\nb = 15<br \/>\ny = 30x + 15<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_107-300x287.png\" alt=\"BIM 8th Grade Solution Key Ch 4 img_107\" width=\"300\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_107-300x287.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Ch-4-img_107.png 754w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>b. Did you and your friend start running from the same spot? Explain your reasoning.<br \/>\nAnswer:<br \/>\nThe distance between you and your friend in the initial moment is b = 15 meters. So you are ahead your friend by 15 meters at the starting point.<\/p>\n<h3><a id=\"Writing_Equations_in_Point_Slope_Form_Homework_&amp;_Practice_4.7\"><\/a>Writing Equations in Point-Slope Form Homework &amp; Practice 4.7<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write an equation in slope-intercept form of the line that passes through the given points.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-7.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 7\" width=\"164\" height=\"74\" \/><br \/>\nAnswer:<br \/>\nSlope(m) = (5 &#8211; 4)\/(0 &#8211; (-2))<br \/>\n= 1\/2<br \/>\nm = 1\/2<br \/>\nBecause y = 5 when x = 0, the y &#8211; intercept is 5.<br \/>\ny = mx + b<br \/>\ny = 1\/2 x + 5<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 8\" width=\"142\" height=\"144\" \/><br \/>\nAnswer:<br \/>\nSlope(m) = (5 &#8211; (-1))\/(2 &#8211; (-2))<br \/>\n= (5 + 1)\/(2 + 2)<br \/>\nm = 6\/4<br \/>\nm = 3\/2<br \/>\nFrom the graph, the line crosses the y &#8211; axis at (0, 2)<br \/>\ny = mx + b<br \/>\ny = 3\/2 x + 2<\/p>\n<p><strong>Solve the equation. Check your solution, if possible.<\/strong><br \/>\nQuestion 3.<br \/>\n2x + 3 = 2x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n2x + 3 = 2x<br \/>\n3 = 2x &#8211; 2x<br \/>\n3 \u2260 0<\/p>\n<p>Question 4.<br \/>\n6x &#8211; 7 = 1 &#8211; 3x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n6x &#8211; 7 = 1 &#8211; 3x<br \/>\n6x + 3x = 1 + 7<br \/>\n9x = 8<br \/>\nx = 8\/3<\/p>\n<p>Question 5.<br \/>\n0.1x &#8211; 1 = 1.2x &#8211; 5.4<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n0.1x &#8211; 1 = 1.2x &#8211; 5.4<br \/>\n0.1x &#8211; 1.2x = 1 &#8211; 5.4<br \/>\n-1.1x = -4.4<br \/>\nx = 4<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><\/p>\n<p><strong>WRITING AN EQUATION<\/strong> The value of a new car decreases $4000 each year. After 3 years, the car is worth $18,000. (See Exploration 2, p. 179.)<br \/>\nQuestion 6.<br \/>\nDraw a graph that shows the value of the car after t years.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_111-300x205.png\" alt=\"BIM 8th Grade Solution Key Chapter 4 img_111\" width=\"300\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_111-300x205.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_111-768x524.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-Chapter-4-img_111.png 1001w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nWrite an equation that represents the value V of the car after t years.<br \/>\nAnswer:<br \/>\ny = -4000t + b<br \/>\nwhere b is the original price<br \/>\n18,000 = -4000(3) + b<br \/>\n18,000 + 12,000 = b<br \/>\nb = 30,000<br \/>\ny = -4000t + 30,000<\/p>\n<p><strong>WRITING AN EQUATION<\/strong> Write an equation in point-slope form of the line that passes through the given point and has the given slope.<br \/>\nQuestion 8.<br \/>\n(3, 0); m = &#8211;\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (0) = -2\/3(x &#8211; 3)<br \/>\ny &#8211; 0 = -2\/3(x &#8211; 3)<\/p>\n<p>Question 9.<br \/>\n(4, 8); m = \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (8) = 3\/4(x &#8211; 4)<br \/>\ny &#8211; 8 = 3\/4(x &#8211; 4)<\/p>\n<p>Question 10.<br \/>\n(1, -3); m = 4<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-3) = 4(x &#8211; 1)<br \/>\ny + 3 = 4(x &#8211; 1)<\/p>\n<p>Question 11.<br \/>\n(7, -5); m = &#8211;\\(\\frac{1}{7}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-5) = &#8211;\\(\\frac{1}{7}\\)(x &#8211; 7)<br \/>\ny + 5 = &#8211;\\(\\frac{1}{7}\\)(x &#8211; 7)<\/p>\n<p>Question 12.<br \/>\n(3, 3); m = \\(\\frac{5}{3}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (3) = \\(\\frac{5}{3}\\)(x &#8211; 3)<br \/>\ny &#8211; 3 = \\(\\frac{5}{3}\\)(x &#8211; 3)<\/p>\n<p>Question 13.<br \/>\n(-1, -4); m = -2<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-4) = -2(x &#8211; (-1))<br \/>\ny + 4 = -2(x + 1)<\/p>\n<p><strong>WRITING AN EQUATION<\/strong> Write an equation in slope-intercept form of the line that passes through the given points.<br \/>\nQuestion 14.<br \/>\n(-1, -1), (1, 5)<br \/>\nAnswer:<br \/>\nSlope(m) = (5 &#8211; (-1))\/(2 &#8211; (-1))<br \/>\n= (5 + 1)\/(1 + 1)<br \/>\nm = 6\/2<br \/>\nm = 3<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (5) = 3(x &#8211; (1))<br \/>\ny &#8211; 5 = 3x &#8211; 3<br \/>\ny = 3x + 2<\/p>\n<p>Question 15.<br \/>\n(2, 4), (3, 6)<br \/>\nAnswer:<br \/>\nSlope(m) = (6 &#8211; 4)\/(3 &#8211; 2)<br \/>\nm = 2\/1<br \/>\nm = 2<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (4) = 2(x &#8211; (2))<br \/>\ny &#8211; 4 = 2x &#8211; 4<br \/>\ny = 2x<\/p>\n<p>Question 16.<br \/>\n(-2, 3), (2, 7)<br \/>\nAnswer:<br \/>\nSlope(m) = (7 &#8211; (3))\/(2 &#8211; (-2))<br \/>\n= (7 &#8211; 3)\/(2 + 2)<br \/>\nm = 4\/4<br \/>\nm = 1<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (3) = 1(x &#8211; (-2))<br \/>\ny &#8211; 3 = x + 2<br \/>\ny = x + 5<\/p>\n<p>Question 17.<br \/>\n(4, 1), (8, 2)<br \/>\nAnswer:<br \/>\nSlope(m) = (2 &#8211; (1))\/(8 &#8211; (4))<br \/>\n= (2 &#8211; 1)\/(8 &#8211; 4)<br \/>\nm = 1\/4<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (1) = 1\/4(x &#8211; (4))<br \/>\ny &#8211; 1 = 1\/4 x &#8211; 1<br \/>\ny = 1\/4 x<\/p>\n<p>Question 18.<br \/>\n(-9, 5), (-3, 3)<br \/>\nAnswer:<br \/>\nSlope(m) = (3 &#8211; (5))\/(-3 &#8211; (-9))<br \/>\n= (3 &#8211; 5)\/(-3 + 9)<br \/>\nm = -2\/6<br \/>\nm = -1\/3<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (3) = -1\/3(x + 3)<br \/>\ny &#8211; 3 = -1\/3 x &#8211; 1<br \/>\ny = -1\/3 x + 2<\/p>\n<p>Question 19.<br \/>\n(1, 2), (-2, -1)<br \/>\nAnswer:<br \/>\nSlope(m) = (2 &#8211; (1))\/(8 &#8211; (4))<br \/>\n= (-1 &#8211; 2)\/(-2 &#8211; 1)<br \/>\nm = -3\/-3<br \/>\nm = 1<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (2) = 1(x &#8211; (1))<br \/>\ny &#8211; 2 = x &#8211; 1<br \/>\ny = x + 1<\/p>\n<p>Question 20.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nAt 0\u00b0 C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by \\(\\frac{2}{25}\\). Write an equation that represents the volume of the gas in terms of the temperature.<br \/>\nAnswer:<br \/>\nThe equation modeling the situation has the form:<br \/>\nV = mT + b<br \/>\nm = 2\/25<br \/>\n22 = 2\/25(0) + b<br \/>\nb = 22<br \/>\nV = 2\/25 T + 22<\/p>\n<p><strong>WRITING AN EQUATION<\/strong> Write an equation of the line that passes through the given points in any form. Explain your choice of form.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-9.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 9\" width=\"140\" height=\"143\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (2.5 &#8211; 1.5)\/(0 &#8211; (-1))<br \/>\n= 1\/1<br \/>\n= 1<br \/>\nBecause the line crosses the y &#8211; axis at (0, 2.5), the y &#8211; intercept is 2.5<br \/>\ny = mx + b<br \/>\ny = (1)x + 2.5<br \/>\ny = x + 2.5<\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-10.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 10\" width=\"139\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (3.5 &#8211; 1.5)\/(2 &#8211; (1))<br \/>\n= 2\/1<br \/>\n= 2<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (1.5) = 2(x &#8211; (1))<br \/>\ny &#8211; 1.5 = 2x &#8211; 2<br \/>\ny = 2x &#8211; 0.5<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 11\" width=\"147\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-1.5 &#8211; 4.5)\/(1 &#8211; (-1))<br \/>\n= -6\/2<br \/>\n= -3<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-1.5) = -3(x &#8211; (1))<br \/>\ny + 1.5 = -3x + 3<br \/>\ny = -3x + 1.5<\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 12\" width=\"115\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (-0.5 &#8211; 3.5)\/(1 &#8211; (-1))<br \/>\n= -4\/2<br \/>\n= -2<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (-0.5) = -2(x &#8211; (1))<br \/>\ny + 0.5 = -2x &#8211; 2<br \/>\ny = -2x &#8211; 2.5<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-13.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 13\" width=\"93\" height=\"126\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (1 &#8211; (-1))\/(0 &#8211; (-3))<br \/>\n= (1 + 1)\/(0 + 3)<br \/>\n= 2\/3<br \/>\nBecause y = 1 when x = 0, the y &#8211; intercept is 1.<br \/>\ny = mx + b<br \/>\ny = 2\/3 x + 1<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-14.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 14\" width=\"97\" height=\"123\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\n= (4 &#8211; 6)\/(-3 &#8211; (-7))<br \/>\n= -2\/4<br \/>\n= -1\/2<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; (2) = -1\/2(x &#8211; (1))<br \/>\ny &#8211; 2 = -1\/2x + 1\/2<br \/>\ny = -1\/2 x + 5\/2<\/p>\n<p>Question 27.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite an equation of the line that passes through the point (8, 2) and is parallel to the graph of the equation y = 4x &#8211; 3.<br \/>\nAnswer:<br \/>\ny = 4x &#8211; 3<br \/>\nComparing the given equation with y = mx + b, we get<br \/>\nm = 4<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 2 = 4(x &#8211; 8)<br \/>\ny &#8211; 2 = 4x &#8211; 32<br \/>\ny = 4x &#8211; 32 + 2<br \/>\ny = 4x &#8211; 30<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the amount y (in fluid ounces) of carpet cleaner in a tank after x minutes of cleaning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 15\" width=\"90\" height=\"132\" \/><br \/>\na. Write an equation that represents the amount of cleaner x in the tank after minutes.<br \/>\nb. How much cleaner is in the tank when the cleaning begins?<br \/>\nc. After how many minutes is the tank empty? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAccording to Dolbear\u2019s law, you can predict the temperature T (in degrees Fahrenheit) by counting the number x of chirps made by a snowy tree cricket in 1 minute.When the temperature is 50\u00b0F, a cricket chirps 40 times in 1 minute. For each rise in temperature of 0.25\u00b0F, the cricket makes an additional chirp each minute.<br \/>\na. You count 100 chirps in 1 minute. What is the temperature?<br \/>\nb. The temperature is 96\u00b0F.How many chirps do you expect the cricket to make? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe Leaning Tower of Pisa in Italy was built between 1173 and 1350.<br \/>\na. Write an equation that represents the yellow line.<br \/>\nb. The tower is 56 meters tall. How far from the center is the top of the tower? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 16\" width=\"214\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-16.png 214w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-16-206x300.png 206w\" sizes=\"(max-width: 214px) 100vw, 214px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_Connecting_Concepts\"><\/a>Graphing and Writing Linear Equations Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nEvery item in a retail store is on sale for 40% off. Write and graph an equation that represents the sale price of an item that has an original price of x dollars.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cc-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cc 1\" width=\"201\" height=\"143\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know the percent discount of items in a retail store.You are asked to write and graph an equation that represents the sale price of an item that has an original price of x dollars.<br \/>\nMake a plan.<br \/>\nSelling an item for 40% off is the same as selling an item for 60% of its original price. Use this information to write and graph an equation that represents the situation.<br \/>\nSolve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<br \/>\n40% = 0.40 and to find a percent of a number you multiply the number by the percent in decimal form.<br \/>\nSo, the equation is d = 0.4p<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-img_111-300x89.png\" alt=\"BIM 8th Grade Answers img_111\" width=\"300\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-img_111-300x89.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-img_111-768x228.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Answers-img_111.png 888w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\nTwo supplementary angles have angle measures of x\u00b0 and y\u00b0. Write and graph an equation that represents the relationship between the measures of the angles.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nA mechanic charges a diagnostic fee plus an hourly rate. The table shows the numbers of hours worked and the total costs for three customers.A fourth customer pays $285. Find the number of hours that the mechanic worked for the fourth customer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cc-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cc 2\" width=\"280\" height=\"77\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Anatomy of a Hurricane<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cHurricane!\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-33133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cc-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cc 3\" width=\"341\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cc-3.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cc-3-300x160.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_Chapter_Review\"><\/a>Graphing and Writing Linear Equations Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><br \/>\nWrite the definition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations cr 1\" width=\"561\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-1-300x44.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><br \/>\nYou can use a Definition and Example Chart to organize information about a concept. Here is an example of a Definition and Example Chart for the vocabulary term linear equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations cr 2\" width=\"392\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-2.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-2-300x207.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/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-33388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-3.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations cr 3\" width=\"288\" height=\"346\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-3.png 288w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-cr-3-250x300.png 250w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><br \/>\n1. slope<br \/>\n2. slope of parallel lines<br \/>\n3. proportional relationship<br \/>\n4. slope-intercept form<br \/>\n5. standard form<br \/>\n6. point-slope form<\/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-33134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 1\" width=\"580\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-1.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-1-300x34.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p><strong>4.1 Graphing Linear Equations (pp. 141\u2013146)<\/strong><br \/>\nLearning Target: Graph linear equations.Graph the linear equation.<\/p>\n<p>Question 1.<br \/>\ny = \\(\\frac{3}{5}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_112-300x207.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_112\" width=\"300\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_112-300x207.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_112.png 613w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 2.<br \/>\ny = -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_113-300x193.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_113\" width=\"300\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_113-300x193.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_113.png 527w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\ny = 9 &#8211; x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_114-300x254.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_114\" width=\"300\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_114-300x254.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_114.png 653w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 4.<br \/>\ny = -0.25x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_115-300x253.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_115\" width=\"300\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_115-300x253.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_115.png 511w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\ny = \\(\\frac{2}{3}\\)x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_116-300x246.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_116\" width=\"300\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_116-300x246.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_116.png 521w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 6.<br \/>\nx = -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_117-300x224.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_117\" width=\"300\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_117-300x224.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_117.png 479w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nThe equation y = 0.53x + 3 represents the cost y (in dollars) of riding in a taxi x miles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-2.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 2\" width=\"213\" height=\"117\" \/><br \/>\na. Use a graph to estimate how much it costs to ride 5.25 miles in a taxi.<br \/>\nb. Use the equation to find exactly how much it costs to ride 5.25 miles in a taxi.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_118-300x207.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_118\" width=\"300\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_118-300x207.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_118-1024x707.png 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_118-768x530.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_118.png 1037w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny = 0.5x + 3<br \/>\ny = 0.5(5.25) + 3<br \/>\ny \u2248 5.6<\/p>\n<p>Question 8.<br \/>\nThe equation y = 9.5x represents the earnings y (in dollars) of an aquarium gift shop employee that works x hours.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-8.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 8\" width=\"185\" height=\"273\" \/><br \/>\na. Graph the linear equation.<br \/>\nb. How much does the employee earn for working 40 hours?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_119-275x300.png\" alt=\"Bigideas Math Answers 8th Grade chapter 4 img_119\" width=\"275\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_119-275x300.png 275w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-Math-Answers-8th-Grade-chapter-4-img_119.png 686w\" sizes=\"(max-width: 275px) 100vw, 275px\" \/><br \/>\nDetermine y for x = 40:<br \/>\ny = 9.5x<br \/>\ny = 9.5(40) = 380<\/p>\n<p>Question 9.<br \/>\nIs y = x<sup>2<\/sup> a linear equation? Explain your reasoning.<br \/>\nAnswer:<br \/>\ny = x<sup>2<\/sup><br \/>\nThe graph of the given equation passes through the origin, but is not linear, therefore it is not a linear equation.<br \/>\nSo, the answer is no.<\/p>\n<p>Question 10.<br \/>\nThe sum S of the exterior angle measures of a polygon with n sides is S = 360\u00b0.<br \/>\na. Plot four points (n, S) that satisfy the equation. Is the equation a linear equation? Explain your reasoning.<br \/>\nb. Does the value n = 2 make sense in the context of the problem? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_120-300x236.png\" alt=\"8th Grade Big Ideas Math Answer Key Chapter 4 img_120\" width=\"300\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_120-300x236.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_120-768x605.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_120.png 877w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe value n = 2 does not make sense in the context of the problem because a polygon has at least 3 sides.<\/p>\n<p><strong>4.2 Slope of a Line (pp. 147\u2013154)<\/strong><br \/>\nLearning Target: Find and interpret the slope of a line.<\/p>\n<p><strong>Describe the slope of the line. Then find the slope of the line.<\/strong><br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-11.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 11\" width=\"172\" height=\"167\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (3, 1)<br \/>\n(x2, y2) = (-3, -3)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-3 &#8211; 1)\/(-3 &#8211; 3)<br \/>\nm = -4\/-6<br \/>\nm = 2\/3<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-12.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 12\" width=\"170\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-12.png 170w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-12-150x150.png 150w\" sizes=\"(max-width: 170px) 100vw, 170px\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (0, 4)<br \/>\n(x2, y2) = (2, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 4)\/(2 &#8211; 0)<br \/>\nm = -6\/2<br \/>\nm = -3<br \/>\nThe slope is negative<\/p>\n<p><strong>Find the slope of the line through the given points.<\/strong><br \/>\nQuestion 13.<br \/>\n(-5, 4), (8, 4)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-5, 4)<br \/>\n(x2, y2) = (8, 4)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (4 &#8211; 4)\/(8 &#8211; (-5))<br \/>\nm = 0\/13<br \/>\nm = 0<\/p>\n<p>Question 14.<br \/>\n(-3, 5), (-3, 1)<br \/>\nAnswer:<br \/>\n(x1, y1) = (-3, 5)<br \/>\n(x2, y2) = (-3, 1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (1 &#8211; 5)\/(-3 + 3)<br \/>\nm = -4\/0<br \/>\nm = undefined<\/p>\n<p><strong>The points in the table lie on a line. Find the slope of the line.<\/strong><br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-15.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 15\" width=\"205\" height=\"55\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (0, -1)<br \/>\n(x2, y2) = (1, 0)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (0 &#8211; (-1))\/(1 &#8211; 0)<br \/>\nm = 1\/1<br \/>\nm = 1<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-16.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 16\" width=\"209\" height=\"61\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-2, 3)<br \/>\n(x2, y2) = (0, 4)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (4 &#8211; 3)\/(0 &#8211; (-2))<br \/>\nm = 1\/2<\/p>\n<p>Question 17.<br \/>\nHow do you know when two lines are parallel? Use an example to justify your answer.<br \/>\nAnswer:<br \/>\nTwo lines are parallel when their slopes are the same. In order for the two lines not to coincide, we must add the condition that their y &#8211; intercepts.<br \/>\nExample 1:<br \/>\nd1: y = 3x &#8211; 6<br \/>\nd2: 3x &#8211; y = 6<br \/>\nThe lines d1 and d2 have the same slope and the same y &#8211; intercept, therefore they coincide.<\/p>\n<p>Question 18.<br \/>\nDraw a line through the point (-1, 2) that is parallel to the graph of the line in Exercise 11.<br \/>\nAnswer:<br \/>\ny = 2\/3 x &#8211; 1<br \/>\nA (-1, 2)<br \/>\ny = 2\/3 x + b<br \/>\ny = 2\/3 (-1) + b<br \/>\nb = 8\/3<br \/>\nThe equation of d1 is:<br \/>\ny = 2\/3 x + 8\/3<br \/>\nDetermine the x intercept of d1:<br \/>\n0 = 2\/3 x + 8\/3<br \/>\n0 = 2x + 8<br \/>\n2x = -8<br \/>\nx = -8\/2<br \/>\nx = -4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-ch-4-img_121-300x251.png\" alt=\"Bigideas math answers grade 8 ch 4 img_121\" width=\"300\" height=\"251\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-ch-4-img_121-300x251.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-ch-4-img_121-768x642.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Bigideas-math-answers-grade-8-ch-4-img_121.png 775w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>4.3 Graphing Proportional Relationships (pp. 155\u2013160)<\/strong><br \/>\nLearning Target: Graph proportional relationships.<\/p>\n<p>Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.<br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-19.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 19\" width=\"167\" height=\"156\" \/><br \/>\nAnswer:<br \/>\nx and y are not in a proportional relationship because the line does not pass through the origin.<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-20.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 20\" width=\"163\" height=\"167\" \/><br \/>\nAnswer:<br \/>\nx and y are in a proportional relationship because the line does passes through the origin.<br \/>\nDetermine the slope k using two points from the graph<br \/>\nk = (10 &#8211; 0)\/(2 &#8211; 0)<br \/>\nk = 10\/2<br \/>\nk = 5x<\/p>\n<p>Question 21.<br \/>\nThe cost y (in dollars) to provide food for guests at a dinner party is proportional to the number x of guests attending the party. It costs $30 to provide food for 4 guests.<br \/>\na. Write an equation that represents the situation.<br \/>\nb. Interpret the slope of the graph of the equation.<br \/>\nc. How much does it cost to provide food for 10 guests? Justify your answer.<br \/>\nAnswer:<br \/>\ny = kx<br \/>\n30 = 4k<br \/>\nk = 30\/4<br \/>\nk = 7.5<br \/>\ny = 7.5x<br \/>\nb. The slope 7.5 represents the unit cost for a guest.<br \/>\ny = 7.5 \u00d7 10<br \/>\ny = 75<br \/>\nc. Determine y for x = 10<br \/>\nSo it costs $75 to provide food for 10 guests.<\/p>\n<p>Question 22.<br \/>\nThe distance y (in miles) you run after weeks is represented by the equation y =8x. Graph the equation and interpret the slope.<br \/>\nAnswer:<br \/>\ny = 8x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_122-300x214.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_122\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_122-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_122-768x549.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_122.png 877w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 23.<br \/>\nYou research that hair grows 15 centimeters per year on average. The table shows your friend&#8217;s hair growth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-23.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 23\" width=\"261\" height=\"83\" \/><br \/>\na. Does your friend&#8217;s hair grow faster than average? Explain.<\/p>\n<p>Answer:<br \/>\nThe rate of growth on average is<br \/>\n15\/12 = 1.25 cm\/month<br \/>\nThe slope\/rate of growth for your friend is<br \/>\n(6 &#8211; 3)\/(4 &#8211; 2) = 3\/2 = 1.5 cm\/month<br \/>\nAs 1.5 &gt; 1.25, your friends hair grows faster than average.<\/p>\n<p>b. In the same coordinate plane, graph the average hair growth and the hair growth of your friend. Compare and interpret the steepness of each of the graphs.<br \/>\nAnswer:<br \/>\nThe equation for the average growth is<br \/>\ny = 1.25x<br \/>\nThe equation for the friends growth is<br \/>\ny = 1.5 x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_123-300x175.png\" alt=\"Big Ideas Math 8th Grade Answer Key for Chapter 4 img_123\" width=\"300\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_123-300x175.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_123-768x448.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-8th-Grade-Answer-Key-for-Chapter-4-img_123.png 1016w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>4.4 Graphing Linear Equations in Slope-Intercept Form (pp. 161\u2013166)<\/strong><br \/>\nLearning Target: Graph linear equations in slope-intercept form.<\/p>\n<p><strong>Find the slope and the -intercept of the graph of the linear equation.<\/strong><br \/>\nQuestion 24.<br \/>\ny = -4x + 1<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nslope = -4 and y &#8211; intercept = 1<\/p>\n<p>Question 25.<br \/>\ny = \\(\\frac{2}{3}\\)x &#8211; 12<br \/>\nAnswer:<br \/>\ny = mx + b<br \/>\nslope = \\(\\frac{2}{3}\\) and y &#8211; intercept = -12<\/p>\n<p>Question 26.<br \/>\ny &#8211; 7 = 0.5x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny &#8211; 7 = 0.5x<br \/>\ny = 0.5x + 7<br \/>\nslope = 0.5 and y &#8211; intercept = 7<\/p>\n<p><strong>Graph the linear equation. Identify the -intercept.<\/strong><br \/>\nQuestion 27.<br \/>\ny = 2x &#8211; 6<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = 2x &#8211; 6<br \/>\nComparing the above equation with slope &#8211; intercept equation<br \/>\nslope = 2, y &#8211; intercept = -6<br \/>\nSlope = rise\/run = 2\/1<br \/>\nPlot the point that is 1 unit right and 2 units up from (0, -6) = (1, -4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_124-300x267.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_124\" width=\"300\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_124-300x267.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_124.png 521w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line crosses the x &#8211; axis at (3, 0)<br \/>\nSo, the x &#8211; intercept is 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_125-300x275.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_125\" width=\"300\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_125-300x275.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_125.png 523w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 28.<br \/>\ny = -4x + 8<br \/>\nAnswer:<br \/>\ny = -4x + 8<br \/>\nslope = -4 and y &#8211; intercept = 8<br \/>\nSo plot (0, 8)<br \/>\nSlope = rise\/run = -4\/1<br \/>\nplot the point that is 1 unit right and 4 units down from (0, 8) = (1, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_126-219x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_126\" width=\"219\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_126-219x300.png 219w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_126.png 409w\" sizes=\"(max-width: 219px) 100vw, 219px\" \/><br \/>\nThe line crosses the x- axis at (2, 0)<br \/>\nSo the x &#8211; intercept is 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_127-231x300.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_127\" width=\"231\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_127-231x300.png 231w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_127.png 421w\" sizes=\"(max-width: 231px) 100vw, 231px\" \/><\/p>\n<p>Question 29.<br \/>\ny = -x &#8211; 8<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = -x &#8211; 8<br \/>\ncomparing the above equation with sloope &#8211; intercept equation.<br \/>\nSlope = -1 and y &#8211; intercept = -8<br \/>\nSlope = rise\/run = -1\/1<br \/>\nPlot the point that is 1 unit right and 1 unit down from (0, -8) = (1, -9)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_128-300x238.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_128\" width=\"300\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_128-300x238.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_128.png 649w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe line crosses the x-axis at (-8, 0)<br \/>\nSo, the intercept is -8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_129-300x234.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_129BIM Grade 8 Answers Chapter 4 img_129\" width=\"300\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_129-300x234.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_129.png 655w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 30.<br \/>\nThe cost y (in dollars) of one person buying admission to a fair and going on x rides is y = x + 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-30.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 30\" width=\"214\" height=\"234\" \/><br \/>\na. Graph the equation.<br \/>\nb. Interpret the y-intercept and the slope.<br \/>\nAnswer:<br \/>\ny = x + 12<br \/>\nComparing the above equation with slope &#8211; intercept equation.<br \/>\nSlope = 1 and y &#8211; intercept = 12<br \/>\nSo plot (0, 20)<br \/>\nSlope = rise\/run = 1\/1<br \/>\nPlot the point that is 1 unit right and 1 unit up from (0, 12) = (1, 13)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_130-300x262.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_130\" width=\"300\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_130-300x262.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_130.png 533w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe y &#8211; intercept is 12 so the initial cost of admission is $12.<br \/>\nThe slope is 1 so for each ride the cost of the person increases $1 per ride.<\/p>\n<p>Question 31.<br \/>\nGraph the linear equation with slope -5 and y-intercept 0.<br \/>\nAnswer:<br \/>\ny &#8211; intercept = 0. So plot (0, 0)<br \/>\nPlot the point that is 1 unit right and 5 unit down from (0, 0) = (1, -5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_131-300x263.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_131\" width=\"300\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_131-300x263.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_131.png 469w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>4.5 Graphing Linear Equations in Standard Form (pp. 167\u2013172)<\/strong><br \/>\nLearning Target: Graph linear equations in standard form.<\/p>\n<p><strong>Write the linear equation in slope-intercept form.<\/strong><br \/>\nQuestion 32.<br \/>\n4x + 2y = -12<br \/>\nAnswer:<br \/>\n4x + 2y = -12<br \/>\n2y = -12 &#8211; 4x<br \/>\ny = -6 &#8211; 2x<br \/>\ny = -2x &#8211; 6<\/p>\n<p>Question 33.<br \/>\nx &#8211; y = \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\nx &#8211; y = \\(\\frac{1}{4}\\)<br \/>\ny = x &#8211; \\(\\frac{1}{4}\\)<\/p>\n<p><strong>Graph the linear equation.<\/strong><br \/>\nQuestion 34.<br \/>\n\\(\\frac{1}{4}\\)x + y = 3<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{4}\\)x + y = 3<br \/>\ny = 3 &#8211; \\(\\frac{1}{4}\\)x<br \/>\ny = &#8211;\\(\\frac{1}{4}\\)x + 3<br \/>\nSlope = &#8211;\\(\\frac{1}{4}\\) and y &#8211; intercept = 3<br \/>\nSo plot (0, 3)<br \/>\nSlope = rise\/run = &#8211;\\(\\frac{1}{4}\\)<br \/>\nPlot the point that is 4 units right and 1 unit down from (0, 3) = (4, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_132-300x239.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 img_132\" width=\"300\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_132-300x239.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_132.png 531w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 35.<br \/>\n-4x + 2y = 8<br \/>\nAnswer:<br \/>\n-4x + 2y = 8<br \/>\n2y = 8 + 4x<br \/>\ny = 2x + 4<br \/>\nSlope = 2 and y &#8211; intercept = 4<br \/>\nSo plot (0, 4)<br \/>\nSlope = rise\/run = 2\/1<br \/>\nPlot the point that is 1 unit right and 2 units up from (0, 4) = (1, 6)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_133-300x300.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 img_133\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_133-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_133-150x150.png 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_133.png 419w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 36.<br \/>\nx + 5y = 10<br \/>\nAnswer:<br \/>\nx + 5y = 10<br \/>\n5y = -x + 10<br \/>\ny = -1\/5 x + 2<br \/>\nSlope = -1\/5 and y &#8211; intercept = 2<br \/>\nSo, plot (0, 2)<br \/>\nSlope = rise\/run = -1\/5<br \/>\nPlot the point that is 5 unit right and 1 unit down from (0, 2) = (5, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_134-300x182.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 img_134\" width=\"300\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_134-300x182.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_134.png 639w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 37.<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + \\(\\frac{1}{8}\\)y = \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + \\(\\frac{1}{8}\\)y = \\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{1}{8}\\)y = \\(\\frac{3}{4}\\)\u00a0 + \\(\\frac{1}{2}\\)x<br \/>\ny = 4x + 6<br \/>\nSlope = 4 and y &#8211; intercept = 6<br \/>\nSo plot (0, 6)<br \/>\nSlope = rise\/run = 4\/1<br \/>\nPlot the point that is 1 unit right and 4 units up from (0, 6) = (1, 10)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_135-257x300.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 4 img_135\" width=\"257\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_135-257x300.png 257w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-4-img_135.png 523w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\n<p>Question 38.<br \/>\nA dog kennel charges $30 per night to board your dog and $6 for each hour of playtime. The amount of money you spend is given by 30x + 6y = 180, where x is the number of nights and y is the number of hours of playtime. Graph the equation and interpret the intercepts.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA dog kennel charges $30 per night to board your dog and $6 for each hour of playtime.<br \/>\nThe amount of money you spend is given by 30x + 6y = 180,<br \/>\nwhere x is the number of nights and y is the number of hours of playtime.<br \/>\n30x + 6y = 180<br \/>\n6y = -30x + 180<br \/>\ny = -5x + 30<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-Grade-8-Chapter-4-img_136-230x300.png\" alt=\"BIM Answers Grade 8 Chapter 4 img_136\" width=\"230\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-Grade-8-Chapter-4-img_136-230x300.png 230w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Answers-Grade-8-Chapter-4-img_136.png 495w\" sizes=\"(max-width: 230px) 100vw, 230px\" \/><br \/>\nThe x &#8211; intercept is 6, which means that the dog can stay for 6 nights when there is no playtime.<br \/>\nThe y &#8211; intercept is 30, which means the dog can play for 30 hours when he does not spend any night at the kennel.<\/p>\n<p><strong>4.6 Writing Equations in Slope-Intercept Form (pp. 173\u2013178)<\/strong><br \/>\nLearning Target: Write equations of lines in slope-intercept form.<\/p>\n<p><strong>Write an equation in slope-intercept form of the line that passes through the given points.<\/strong><br \/>\nQuestion 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-39.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 39\" width=\"144\" height=\"114\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (1 &#8211; (-2))\/(3 &#8211; 0)<br \/>\nm = (1 + 2)\/(3 &#8211; 0)<br \/>\nm = 3\/3<br \/>\nm = 1<br \/>\nWe have to find the y &#8211; intercept because the line crosses the y &#8211; axis at (0, -2)<br \/>\ny = mx + b<br \/>\ny = x &#8211; 2<\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-40.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 40\" width=\"154\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (4 &#8211; 2)\/(0 &#8211; 4)<br \/>\nm = 2\/-4<br \/>\nm = -1\/2<br \/>\nWe have to find the y &#8211; intercept because the line crosses the y &#8211; axis at (0, 4)<br \/>\ny = mx + b<br \/>\ny =-1\/2 x + 4<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-41.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 41\" width=\"98\" height=\"152\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; 1)\/(2 &#8211; 0)<br \/>\nm = -3\/2<br \/>\nWe have to find the y &#8211; intercept because y = 1 when x = 0, the y &#8211; intercept is 1.<br \/>\ny = mx + b<br \/>\ny = -3\/2 x + 1<\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-42.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 42\" width=\"89\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; (-3))\/(1 &#8211; 0)<br \/>\nm = 2\/1<br \/>\nm = 2<br \/>\nWe have to find the y &#8211; intercept because y = -3 when x = 0, the y &#8211; intercept is -3.<br \/>\ny = mx + b<br \/>\ny = 2x + (-3)<br \/>\ny = 2x &#8211; 3<\/p>\n<p>Question 43.<br \/>\nWrite an equation of the line that passes through (0, 8) and (6, 8).<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (8 &#8211; 8)\/(6 &#8211; 0)<br \/>\nm = 0\/6<br \/>\nm = 0<br \/>\nWe have to find the y &#8211; intercept because y = 8 when x = 0, the y &#8211; intercept is 8.<br \/>\ny = mx + b<br \/>\ny = (0) x + 8<br \/>\ny = 8<\/p>\n<p>Question 44.<br \/>\nWrite an equation of the line that passes through (0, -5) and (-5, -5).<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-5 &#8211; (-5))\/(-5 &#8211; 0)<br \/>\nm = 0\/-5<br \/>\nm = 0<br \/>\nWe have to find the y &#8211; intercept because y = -5 when x = 0, the y &#8211; intercept is -5<br \/>\ny = mx + b<br \/>\ny = (0) x + (-5)<br \/>\ny = -5<\/p>\n<p>Question 45.<br \/>\nA construction crew is extending a highway sound barrier that is 13 miles long. The crew builds \\(\\frac{1}{2}\\) of a mile per week. Write an equation in slope -intercept form that represents the length y (in miles) of the barrier after x weeks.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA construction crew is extending a highway sound barrier that is 13 miles long.<br \/>\nThe crew builds \\(\\frac{1}{2}\\) of a mile per week.<br \/>\ny = mx + b<br \/>\nm = \\(\\frac{1}{2}\\)<br \/>\nb = 13<br \/>\ny = \\(\\frac{1}{2}\\)x + 13<\/p>\n<p><strong>4.7 Writing Equations in Point-Slope Form (pp. 179\u2013184)<\/strong><br \/>\nLearning Target: Write equations of lines in point-slope form.<\/p>\n<p><strong>Write an equation in point-slope form of the line that passes through the given point and has the given slope.<\/strong><br \/>\nQuestion 46.<br \/>\n(4, 4); m = 3<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\nSubstitute m value, x and y value in the equation<br \/>\ny &#8211; (4) = 3(x &#8211; 4)<br \/>\ny &#8211; 4 = 3(x &#8211; 4)<\/p>\n<p>Question 47.<br \/>\n(2, -8); m = &#8211;\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\nSubstitute m value, x and y value in the equation<br \/>\ny &#8211; (-8) = &#8211;\\(\\frac{2}{3}\\)(x &#8211; 2)<br \/>\ny + 8 = &#8211;\\(\\frac{2}{3}\\)(x &#8211; 2)<\/p>\n<p>Write an equation in slope-intercept form of the line that passes through the given points.<br \/>\nQuestion 48.<br \/>\n(-4, 2), (6, -3)<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-3 &#8211; 2)\/(6 &#8211; (-4))<br \/>\nm = -5\/10<br \/>\nm = -1\/2<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\nSubstitute m value, x and y value in the equation<br \/>\ny &#8211; 2 = &#8211;\\(\\frac{1}{2}\\)(x &#8211; (-4))<br \/>\ny &#8211; 2 = &#8211;\\(\\frac{1}{2}\\)(x + 4)<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-49.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 49\" width=\"165\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (5 &#8211; 1)\/(3 &#8211; 2)<br \/>\nm = 4\/1<br \/>\nm = 4<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\nSubstitute m value, x and y value in the equation<br \/>\ny &#8211; (-3) = 4(x &#8211; 1)<br \/>\ny + 3 = 4x &#8211; 4<br \/>\ny = 4x &#8211; 7<\/p>\n<p>Question 50.<br \/>\nThe table shows your elevation y (in feet) on a ski slope after x minutes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-4-Graphing-and-Writing-Linear-Equations-4.7-cr-50.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 4 Graphing and Writing Linear Equations 4.7 cr 50\" width=\"173\" height=\"72\" \/><br \/>\na. Write an equation that represents your elevation after x minutes.<\/p>\n<p>Answer:<br \/>\nm = (600 &#8211; 800)\/(2 &#8211; 1)<br \/>\nm = -200<br \/>\n800 = -200(1) + b<br \/>\n800 = -200 + b<br \/>\n800 + 200 = b<br \/>\nb = 1000 feet<\/p>\n<p>b. What is your starting elevation?<\/p>\n<p>Answer:<br \/>\nThe starting elevation is the y &#8211; intercept<br \/>\nb = 1000 feet<\/p>\n<p>c. After how many minutes do you reach the bottom of the ski slope? Justify your answer.<br \/>\nAnswer:<br \/>\n0 = -200x + 1000<br \/>\n0 &#8211; 1000 = -200x<br \/>\n-1000 = -200x<br \/>\n200x = 1000<br \/>\nx = 5 minutes<\/p>\n<p>Question 51.<br \/>\nA company offers cable television at$29.95 per month plus a one-time installation fee. The total cost for the first six months of service is $214.70. a. Write an equation in point-slope form that represents the total cost you pay for cable television after x months.<br \/>\nb. How much is the installation fee? Justify your answer.<br \/>\nAnswer:<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\nm = 29.95<br \/>\ny &#8211; 214.70 = 29.95(x &#8211; 6)<br \/>\ny &#8211; 214.70 + 214.70 = 29.95x &#8211; 179.97 + 2147.70<br \/>\ny = 29.95x + 35<br \/>\nb = 35<\/p>\n<p>Question 52.<br \/>\nWhen might it be better to represent an equation in point-slope form rather than slope-intercept form? Use an example to justify your answer.<br \/>\nAnswer:<br \/>\nWhen we are given the slope and a point that is the y &#8211; intercept, then the easiest way is to use the slope &#8211; intercept form y = mx + b<br \/>\nExample:<br \/>\nm = 2<br \/>\n(0, 5)<br \/>\ny = 2x + 5<br \/>\nm = 2<br \/>\n(1, 3)<br \/>\ny &#8211; 3 = 2(x &#8211; 1)<br \/>\nEasier when given the slope and a point that is not the y &#8211; intercept.<\/p>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_Practice_Test\"><\/a>Graphing and Writing Linear Equations Practice Test<\/h3>\n<p><strong>Find the slope and the -intercept of the graph of the linear equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 6x &#8211; 5<br \/>\nAnswer:<br \/>\ny = 6x &#8211; 5<br \/>\nSlope = 6 and y &#8211; intercept = -5<\/p>\n<p>Question 2.<br \/>\ny &#8211; 1 = 3x + 8.4<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny &#8211; 1 = 3x + 8.4<br \/>\ny = 3x + 8.4 + 1<br \/>\ny = 3x + 9.4<br \/>\nSlope = 3 and y &#8211; intercept = 9.4<\/p>\n<p>Question 3.<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + 2y = 7<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n&#8211;\\(\\frac{1}{2}\\)x + 2y = 7<br \/>\ny = \\(\\frac{1}{4}\\)x + \\(\\frac{7}{2}\\)<br \/>\nSlope = \\(\\frac{1}{4}\\) and y &#8211; intercept = \\(\\frac{7}{2}\\)<\/p>\n<p>Graph the linear equation.<br \/>\nQuestion 4.<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x &#8211; 5<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x &#8211; 5<br \/>\nSlope = &#8211;\\(\\frac{1}{2}\\) and y &#8211; intercept = -5<br \/>\nSo plot (0, -5)<br \/>\nPlot the point that is 2 units right and 1 unit down from (0, -5) = (2, -6)<br \/>\nDraw a line through the two points.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_108-300x292.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_108\" width=\"300\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_108-300x292.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_108.png 469w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 5.<br \/>\n-3x + 6y = 12<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\n-3x + 6y = 12<br \/>\n6y = 3x + 12<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\nSlope = \\(\\frac{1}{2}\\), y &#8211; intercept = 2<br \/>\nSlope = rise\/run = \\(\\frac{1}{2}\\)<br \/>\nPlot the point that is 2 units right and 1 unit up from (0, 2) = (2, 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_109-300x260.png\" alt=\"BIM Grade 8 Answers Chapter 4 img_109\" width=\"300\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_109-300x260.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-Grade-8-Answers-Chapter-4-img_109.png 423w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 6.<br \/>\ny = \\(\\frac{2}{3}\\)x<br \/>\nAnswer:<br \/>\nGiven the equation<br \/>\ny = \\(\\frac{2}{3}\\)x<br \/>\nSlope = \\(\\frac{2}{3}\\), y &#8211; intercept = 0<br \/>\nSlope = rise\/run = \\(\\frac{2}{3}\\)<br \/>\nPlot the point that is 3 units right and 2 unit up from (0, 0) = (3, 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_109-300x240.png\" alt=\"Big Ideas Math Answers Grade 8 Ch 4 img_109\" width=\"300\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_109-300x240.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Ch-4-img_109.png 413w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 7.<br \/>\nWhich lines are parallel? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-pt-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation pt 7\" width=\"207\" height=\"196\" \/><br \/>\nAnswer:<br \/>\nRed line:<br \/>\n(x1, y1) = (-4, 1)<br \/>\n(x2, y2) = (2, 4)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (4 &#8211; 1)\/(2 &#8211; (-4))<br \/>\nm = 3\/6<br \/>\nm = 1\/2<br \/>\nBlue line:<br \/>\n(x1, y1) = (-4, -1)<br \/>\n(x2, y2) = (2, 0.5)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (0.5 &#8211; (-1))\/(2 &#8211; (-4))<br \/>\nm = 1.5\/6<br \/>\nm = 1\/4<br \/>\nGreen Line:<br \/>\n(x1, y1) = (-2, -4)<br \/>\n(x2, y2) = (2, -2)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-2 &#8211; (-4))\/(2 &#8211; (-2))<br \/>\nm = 2\/4<br \/>\nm = 1\/2<br \/>\nRed lines and Green lines are parallel because both have same slope = 1\/2<\/p>\n<p>Question 8.<br \/>\nThe points in the table lie on a line. Find the slope of the line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-pt-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation pt 8\" width=\"106\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-1, -4)<br \/>\n(x2, y2) = (0, -1)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-1 &#8211; (-4))\/(0 &#8211; (-1))<br \/>\nm = 3\/1<br \/>\nm = 3<\/p>\n<p>Write an equation in slope-intercept form of the line that passes through the given points.<br \/>\nQuestion 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-pt-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation pt 9\" width=\"165\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n(x1, y1) = (-4, 1)<br \/>\n(x2, y2) = (2, 4)<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (-5 &#8211; (-1))\/(3 &#8211; 0)<br \/>\nm = -4\/3<br \/>\nBecause the line crosses the y &#8211; axis at (0, -1), the y &#8211; intercept is -1.<br \/>\ny = mx + b<br \/>\ny = -4\/3x &#8211; 1<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-pt-10.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation pt 10\" width=\"99\" height=\"158\" \/><br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (2 &#8211; 2)\/(0 &#8211; (-2))<br \/>\nm = 0\/2<br \/>\nm = 0<br \/>\nBecause y = 2 when x =0, the y &#8211; intercept is 2.<br \/>\ny = mx + b<br \/>\ny = 2<\/p>\n<p>Question 11.<br \/>\nWrite an equation in point-slope form of the line that passes through (-4, 1) and (4, 3).<br \/>\nAnswer:<br \/>\nm = (y2 &#8211; y1)\/(x2 &#8211; x1)<br \/>\nm = (3 &#8211; 1)\/(4 &#8211; (-4))<br \/>\nm = 2\/8<br \/>\nm = 1\/4<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 1 = 1\/4(x &#8211; (-4))<br \/>\ny &#8211; 1 = 1\/4(x + 4)<\/p>\n<p>Question 12.<br \/>\nThe number y of new vocabulary words that you learn after x weeks is represented by the equation y = 15x.<br \/>\na. Graph the equation and interpret the slope.<br \/>\nb. How many new vocabulary words do you learn after 5 weeks?<br \/>\nc. How many more vocabulary words do you learn after 6 weeks than after 4 weeks?<br \/>\nAnswer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-medium wp-image-79559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_109-300x172.png\" alt=\"8th Grade Big Ideas Math Answer Key Chapter 4 img_109\" width=\"300\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_109-300x172.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_109-1024x588.png 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_109-768x441.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_109.png 1058w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. y = 15 . 5<br \/>\ny = 75 words<br \/>\nc. 15 . 6 &#8211; 15 . 4 = 90 &#8211; 60 = 30 words<\/p>\n<p>Question 13.<br \/>\nYou used $90 worth of paint for a school float. The amount of money you spend is given by 18x + 15y = 90, where x is the number of gallons of blue paint and y is the number of gallons of white paint. Graph the equation and interpret the intercepts.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n18x + 15y = 90<br \/>\n15y = -18x + 90<br \/>\ny = -6\/5 x + 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-79564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_110-300x210.png\" alt=\"8th Grade Big Ideas Math Answer Key Chapter 4 img_110\" width=\"300\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_110-300x210.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_110-768x537.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/8th-Grade-Big-Ideas-Math-Answer-Key-Chapter-4-img_110.png 857w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe x &#8211; intercept is 5 and shows that 5 gallons of blue paint might be bought when no gallon of the white pants is bought.<br \/>\nThe y &#8211; intercept is 6 and shows that 6 gallons of white paint might be bought when no gallon of blue is bought.<\/p>\n<h3><a id=\"Graphing_and_Writing_Linear_Equations_Cumulative_Practice\"><\/a>Graphing and Writing Linear Equations Cumulative Practice<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-1.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 1\" width=\"306\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-1.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-1-254x300.png 254w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nQuestion 1.<br \/>\nWhich equation matches the line shown in the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-2.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 2\" width=\"177\" height=\"168\" \/><br \/>\nA. y =2x &#8211; 2<br \/>\nB. y = 2x + 1<br \/>\nC. y = x &#8211; 2<br \/>\nD. y = x + 1<br \/>\nAnswer:<br \/>\nm = (-2 &#8211; 0)\/(0 &#8211; 1)<br \/>\nm = 2<br \/>\ny = 2x &#8211; 2<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 2.<br \/>\nWhich point lies on the graph of 6x &#8211; 5y = 14?<br \/>\nF. (-4, -1)<br \/>\nG. (-2, 4)<br \/>\nH. (-1, -4)<br \/>\nI. (4, -2)<br \/>\nAnswer:<br \/>\n6x &#8211; 5y = 14<br \/>\nF. 6(-4) &#8211; 5(-1) = 14<br \/>\n-24 + 5 = 14<br \/>\n-19 \u2260 14<br \/>\nG. 6(-2) &#8211; 5(4) = 14<br \/>\n-12 &#8211; 20 = 14<br \/>\n-32 \u2260 14<br \/>\nH. 6(-1) &#8211; 5(-4) = 14<br \/>\n-6 + 20 = 14<br \/>\n14 = 14<br \/>\nThus the correct answer is option H.<\/p>\n<p>Question 3.<br \/>\nYou reflect the triangle in the x-axis. What are the coordinates of the image?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-3.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 3\" width=\"185\" height=\"177\" \/><br \/>\nA. X'(4, 1), Y'(2, 3), Z'(-2, 1)<br \/>\nB. X'(4, -1), Y'(2, -3), Z'(-2, -1)<br \/>\nC. X'(-4, -1), Y(-2, -3), Z'(2, -1)<br \/>\nD. X'(1, 4), Y'(3, 2), Z'(1, -2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-78973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-ch-4-img_108-300x214.png\" alt=\"BIM 8th Grade Solution Key ch 4 img_108\" width=\"300\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-ch-4-img_108-300x214.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-ch-4-img_108-768x547.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/BIM-8th-Grade-Solution-Key-ch-4-img_108.png 876w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 4.<br \/>\nWhich of the following is the equation of a line parallel to the line shown in the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-4.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 4\" width=\"384\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-4.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-4-300x155.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><br \/>\nAnswer:<br \/>\nm = (-4 &#8211; 2)\/(6 &#8211; 4)<br \/>\nm = -6\/2<br \/>\nm = -3<br \/>\nTwo lines parallel if they have the same slope.<br \/>\nFrom the given equations, the one having the slope -3 is y = -3x + 5<br \/>\nThus the correct answer is option H.<\/p>\n<p>Question 5.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-5.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 5\" width=\"232\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n122 = 47 + x<br \/>\n47 + x = 122<br \/>\nx = 122 &#8211; 47<br \/>\nx = 75<\/p>\n<p>Question 6.<br \/>\nAn emergency plumber charges $49.00 plus $70.00 per hour of the repair. A bill to repair your sink is $241.50. This can be modeled by 70.00 h + 49.00 = 241.50, where h represents the number of hours for the repair. How many hours did it take to repair your sink?<br \/>\nA. 2.75 hours<br \/>\nB. 3.45 hours<br \/>\nC. 4.15 hours<br \/>\nD. 13,475 hours<br \/>\nAnswer:<br \/>\n70.00 h + 49.00 = 241.50<br \/>\n70h = 241.50 &#8211; 49<br \/>\n70h = 192.5<br \/>\nh = 2.75 hours<br \/>\nThus the correct answer is option A.<\/p>\n<p>Question 7.<br \/>\nIt costs $40 to rent a car for one day. In addition, the rental agency charges you for each mile driven, as shown in the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-7.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 7\" width=\"354\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-7.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-7-300x151.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><br \/>\nPart A Determine the slope of the line joining the points on the graph.<br \/>\nPart B Explain what the slope represents.<br \/>\nAnswer:<br \/>\nm = (50 &#8211; 40)\/(100 &#8211; 0)<br \/>\nm = 10\/100<br \/>\nm = 0.1<\/p>\n<p>Question 8.<br \/>\nWhat value of makes the equation true?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-8.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 8\" width=\"86\" height=\"67\" \/><br \/>\n7 + 2x = 4x &#8211; 5<br \/>\nAnswer:<br \/>\n7 + 2x = 4x &#8211; 5<br \/>\n2x &#8211; 4x = -5 &#8211; 7<br \/>\n-2x = -12<br \/>\nx = 6<\/p>\n<p>Question 9.<br \/>\nTrapezoid KLMN is graphed in the coordinate plane shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-9.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 9\" width=\"216\" height=\"208\" \/><br \/>\nRotate Trapezoid KLMN 90\u00b0 clockwise about the origin. What are the coordinates of point M&#8217;, the image of point M after the rotation?<br \/>\nF. (-3, -2)<br \/>\nG. (-2, -3)<br \/>\nH. (-2, 3)<br \/>\nI. (3, 2)<br \/>\nAnswer: M'(-3, -2)<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 10.<br \/>\nSolve the formula K = 3M &#8211; 7.<br \/>\nA. M = K + 7<br \/>\nB. M = \\(\\frac{K+7}{3}\\)<br \/>\nC. M = \\(\\frac{K}{3}\\) + 7<br \/>\nD. M = \\(\\frac{K-7}{3}\\)<br \/>\nAnswer:<br \/>\nK = 3M &#8211; 7<br \/>\nK + 7 = 3M<br \/>\nM = \\(\\frac{K+7}{3}\\)<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 11.<br \/>\nWhat is the distance across the canyon?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-33159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-11.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 4 Exponents and Scientific Notation cp 11\" width=\"303\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-11.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-4-Exponents-and-Scientific-Notation-cp-11-300x143.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nF. 3.6 ft<br \/>\nG. 12 ft<br \/>\nH. 40 ft<br \/>\nI. 250 ft<br \/>\nAnswer:<br \/>\n100\/30 = d\/12<br \/>\n3d = 12 \u00d7 10<br \/>\n3d = 120<br \/>\nd = 40 feet<br \/>\nThus the correct answer is option H.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>All the solutions in the above article are beneficial for all the students of middle school students. All the solutions are prepared by the math professionals. The solutions are given clearly with step by step explanations. If you have any doubts regarding the chapter we are always ready to clarify your doubts. All you have to do is to post the comments in the below comment box.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you searching everywhere regarding the Big Ideas Math 8th Grade Answer Key Chapter 4 Graphing and Writing Linear Equations? If so, halt your search as this is the one-stop destination for all your needs. Practice using the Graphing and Writing Linear Equations Big Ideas Math Grade 8 Answers and understand the concepts easily. 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