{"id":6417,"date":"2022-03-26T15:40:35","date_gmt":"2022-03-26T10:10:35","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6417"},"modified":"2022-04-07T12:49:26","modified_gmt":"2022-04-07T07:19:26","slug":"go-math-grade-8-answer-key-chapter-4-nonproportional-relationships","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-4-nonproportional-relationships\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships"},"content":{"rendered":"<p>Are you searching for Go Math 8th Grade Answer Key Chapter 4 Nonproportional Relationships? If yes, then download <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> pdf from here in this article. It helps the students to score good marks in the exams. All the solutions are prepared by the math experts according to the latest edition. Get free access for all topics on Go Math Grade 8 Chapter 4 Nonproportional Relationships from here.<\/p>\n<h2>Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships<\/h2>\n<p>Check the list of the exercises contained in Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships. With the help of this Go Math Grade 8 Chapter 4 Nonproportional Relationships Solution Key students can improve their performance in the tests or assignments. Refer to HMH Go Math Grade 8 Chapter 4 Answer Key to complete your homework in time.<\/p>\n<p><strong>Lesson 1: Representing Linear Nonproportional Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#Representing_Linear_Nonproportional_Relationships_-_Page_No._98\">Representing Linear Nonproportional Relationships &#8211; Page No. 98<\/a><\/li>\n<li><a href=\"#Representing_Linear_Nonproportional_Relationships_\u2013_Page_No._99\">Representing Linear Nonproportional Relationships \u2013 Page No. 99<\/a><\/li>\n<li><a href=\"#Representing_Linear_Nonproportional_Relationships_\u2013_Page_No._100\">Representing Linear Nonproportional Relationships \u2013 Page No. 100<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Determining Slope and y-intercept<\/strong><\/p>\n<ul>\n<li><a href=\"#Determining_Slope_and_y-intercept_\u2013_Page_No._104\">Determining Slope and y-intercept \u2013 Page No. 104<\/a><\/li>\n<li><a href=\"#Determining_Slope_and_y-intercept_\u2013_Page_No._105\">Determining Slope and y-intercept \u2013 Page No. 105<\/a><\/li>\n<li><a href=\"#Determining_Slope_and_y-intercept_\u2013_Page_No._106\">Determining Slope and y-intercept \u2013 Page No. 106<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept<\/strong><\/p>\n<ul>\n<li><a href=\"#Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._110\">Graphing Linear Nonproportional Relationships Using Slope and y-intercept \u2013 Page No. 110<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._111\">Graphing Linear Nonproportional Relationships Using Slope and y-intercept \u2013 Page No. 111<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._112\">Graphing Linear Nonproportional Relationships Using Slope and y-intercept \u2013 Page No. 112<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Proportional and Nonproportional Situations\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Proportional_and_Nonproportional_Situations_\u2013_Page_No._117\">Proportional and Nonproportional Situations \u2013 Page No. 117<\/a><\/li>\n<li><a href=\"#Proportional_and_Nonproportional_Situations_\u2013_Page_No._118\">Proportional and Nonproportional Situations \u2013 Page No. 118<\/a><\/li>\n<li><a href=\"#Proportional_and_Nonproportional_Situations_\u2013_Page_No._119\">Proportional and Nonproportional Situations \u2013 Page No. 119<\/a><\/li>\n<li><a href=\"#Proportional_and_Nonproportional_Situations_\u2013_Page_No._120\">Proportional and Nonproportional Situations \u2013 Page No. 120<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5: Representing Linear Nonproportional Relationships \u2013 Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#Representing_Linear_Nonproportional_Relationships_\u2013_Model_Quiz_\u2013_Page_No._121\">Representing Linear Nonproportional Relationships \u2013 Model Quiz \u2013 Page No. 121<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._122\">Mixed Review \u2013 Page No. 122<\/a><\/li>\n<\/ul>\n<h3><a id=\"Representing_Linear_Nonproportional_Relationships_-_Page_No._98\"><\/a>Guided Practice &#8211; Representing Linear Nonproportional Relationships &#8211; Page No. 98<\/h3>\n<p><strong>Make a table of values for each equation.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 2x + 5<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 1\" width=\"317\" height=\"76\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-13-300x49.png\" alt=\"grade 8 chapter 4 image 13\" width=\"300\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-13-300x49.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-13.png 476w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 2x + 5<br \/>\nChoose several values for x and substitute in the equation to find y.<br \/>\nx = 2(-2) + 5 = 1<br \/>\nx = 2(-1) + 5 = 3<br \/>\nx = 2(0) + 5 = 5<br \/>\nx = 2(1) + 5 = 7<br \/>\nx = 2(2) + 5 = 9<\/p>\n<p>Question 2.<br \/>\ny = \\(\\frac{3}{8}\\)x \u2212 5<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 2\" width=\"320\" height=\"77\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-14-300x54.png\" alt=\"grade 8 chapter 4 image 14\" width=\"300\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-14-300x54.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-14.png 477w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = \\(\\frac{3}{8}\\)x \u2212 5<br \/>\nChoose several values for x and substitute in the equation to find y.<br \/>\nx = 3\/8(-8) &#8211; 5 = -8<br \/>\nx = 3\/8(0) &#8211; 5 = -5<br \/>\nx = 3\/8(8) &#8211; 5 = -2<br \/>\nx = 3\/8(16) &#8211; 5 = 1<br \/>\nx = 3\/8(24) &#8211; 5 = 4<\/p>\n<p><strong>Explain why each relationship is not proportional.<\/strong><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 3\" width=\"306\" height=\"73\" \/><br \/>\nFirst calculate \\(\\frac{y}{x}\\) for the values in the table.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe relationship is not proportional<\/p>\n<p>Explanation:<br \/>\nFind y\/x<br \/>\n3\/0 = undefined<br \/>\n7\/2 = 3.5<br \/>\n11\/4 = 2.75<br \/>\n15\/6 = 2.5<br \/>\n19\/8 = 2.375<br \/>\nThe ratio is not constant, hence relationship is not proportional.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 4\" width=\"221\" height=\"219\" \/><br \/>\n__________________<\/p>\n<p>Answer:<br \/>\nThe graph is a straight line but does not pass through the origin. So, the relationship is not proportional.<\/p>\n<p><strong>Complete the table for the equation. Then use the table to graph the equation.<\/strong><\/p>\n<p>Question 5.<br \/>\ny = x \u2212 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 5\" width=\"313\" height=\"68\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 6\" width=\"216\" height=\"225\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-15-300x47.png\" alt=\"grade 8 chapter 4 image 15\" width=\"300\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-15-300x47.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-15.png 473w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-16-300x279.png\" alt=\"grade 8 chapter 4 image 16\" width=\"300\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-16-300x279.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-16.png 537w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = x &#8211; 1<br \/>\nChoose several values of x and substitute in the equation to find y to draw a table.<br \/>\nx = -2; y = -2 &#8211; 1 = -2<br \/>\nx = -1; y = -1 -1 = -2<br \/>\nx = 0; y = 0 -1 = -1<br \/>\nx = 1; y = 1 &#8211; 1 = 0<br \/>\nx = 2; y = 2 -1 = 1<br \/>\nAlso, Plot the ordered pairs from the table. Then draw a line connecting the points to represent all the possible solutions<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nHow can you choose values for x when making a table of values representing a real world situation?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nWhen choosing values for x in a real-world situation, you choose positive values with an appropriate interval to represent the array of data.<\/p>\n<h3><a id=\"Representing_Linear_Nonproportional_Relationships_\u2013_Page_No._99\"><\/a>Independent Practice &#8211; Representing Linear Nonproportional Relationships &#8211; Page No. 99<\/h3>\n<p><strong>State whether the graph of each linear relationship is a solid line or a set of unconnected points. Explain your reasoning.<\/strong><\/p>\n<p>Question 7.<br \/>\nThe relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSet of unconnected points.<\/p>\n<p>Explanation:<br \/>\nYou cannot buy a fractional part of a lunch.<br \/>\nSet of unconnected points.<\/p>\n<p>Question 8.<br \/>\nThe relationship between time and the distance remaining on a 3-mile walk for someone walking at a steady rate of 2 miles per hour.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nA solid line<\/p>\n<p>Explanation:<br \/>\nThe relationship between time and the distance remaining on a 3-mile walk for someone walking at a steady rate of 2 miles per hour. The distance remaining can be a fraction. The time can be in a fraction as well.<br \/>\nA solid line<\/p>\n<p>Question 9.<br \/>\nAnalyze Relationships<br \/>\nSimone paid $12 for an initial year\u2019s subscription to a magazine. The renewal rate is $8 per year. This situation can be represented by the equation y = 8x + 12, where x represents the number of years the subscription is renewed and y represents the total cost.<br \/>\na. Make a table of values for this situation.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 7\" width=\"617\" height=\"76\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-17-300x50.png\" alt=\"grade 8 chapter 4 image 17\" width=\"300\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-17-300x50.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-17.png 471w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 8x + 12<br \/>\nChoose several values for x and substitute in the equation to find y.<\/p>\n<p>Question 9.<br \/>\nb. Draw a graph to represent the situation. Include a title and axis labels.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-18-300x226.png\" alt=\"grade 8 chapter 4 image 18\" width=\"300\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-18-300x226.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-18.png 653w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nPlot the ordered pairs from the table. Then draw a line connecting the points to represent all the possible solutions<\/p>\n<p>Question 9.<br \/>\nc. Explain why this relationship is not proportional.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 8\" width=\"238\" height=\"225\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIt is not proportional as the graph does not pass through the origin<\/p>\n<p>Explanation:<br \/>\nWhen a relationship is proportional, the graph of the equation passes through the origin.<br \/>\nIt is not proportional as the graph does not pass through the origin<\/p>\n<p>Question 9.<br \/>\nd. Does it make sense to connect the points on the graph with a solid line? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nNo; The subscription is rewened for the entire year and cannot be done for a fraction of the year. The number of years must be a whole numb, so the total cost goes up in $8 increments.<\/p>\n<h3><a id=\"Representing_Linear_Nonproportional_Relationships_\u2013_Page_No._100\"><\/a>Representing Linear Nonproportional Relationships &#8211; Page No. 100<\/h3>\n<p>Question 10.<br \/>\nAnalyze Relationships<br \/>\nA proportional relationship is a linear relationship because the rate of change is constant (and equal to the constant of proportionality). What is required of a proportional relationship that is not required of a general linear relationship?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe ratio between one quantity to the other quantity should be constant for a proportional linear relationship. The graph should be a straight line that passes through the origin.<\/p>\n<p>Question 11.<br \/>\nCommunicate Mathematical Ideas<br \/>\nExplain how you can identify a linear non-proportional relationship from a table, a graph, and an equation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIn a table, the ratios y\/x will not be equal. A graph will not pass through the origin. An equation will be in the form y = mx + b where b is not equal to 0.<\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 12.<br \/>\nCritique Reasoning<br \/>\nGeorge observes that for every increase of 1 in the value of x, there is an increase of 60 in the corresponding value of y. He claims that the relationship represented by the table is proportional. Critique George\u2019s reasoning.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 1: Representing Linear Nonproportional Relationships img 9\" width=\"355\" height=\"75\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe ratio is not constant, hence the relationship cannot be proportional.<\/p>\n<p>Explanation:<br \/>\nFind y\/x<br \/>\n90\/1 = 90<br \/>\n150\/2 = 75<br \/>\n210\/3 = 70<br \/>\n270\/4 = 67.5<br \/>\n330\/5 = 66<br \/>\nThe ratio is not constant, hence the relationship cannot be proportional.<\/p>\n<p>Question 13.<br \/>\nMake a Conjecture<br \/>\nTwo parallel lines are graphed on a coordinate plane. How many of the lines could represent proportional relationships? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nMaximum one<\/p>\n<p>Explanation:<br \/>\nWhen there are two parallel lines, only one can pass through the origin and a line representing a proportional relationship must pass through the origin.<br \/>\nMaximum one<\/p>\n<h3><a id=\"Determining_Slope_and_y-intercept_\u2013_Page_No._104\"><\/a>Guided Practice &#8211; Determining Slope and y-intercept &#8211; Page No. 104<\/h3>\n<p><strong>Find the slope and y-intercept of the line in each graph.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 10\" width=\"219\" height=\"233\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nm = ____________<br \/>\nb = ____________<\/p>\n<p>Answer:<br \/>\nslope m = -2 y-intercept b = 1<br \/>\nm = -2<br \/>\nb = 1<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, 1) and (x2, y2) = (2, -3)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (-3 \u2013 1)\/(2 \u2013 0) = -4\/2 = -2<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 1<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 11\" width=\"226\" height=\"218\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nm = ____________<br \/>\nb = ____________<\/p>\n<p>Answer:<br \/>\nslope m = 5 y-intercept b = -15<br \/>\nm = 5<br \/>\nb = -15<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, -15)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (-15 \u2013 0)\/(0 \u2013 3) = 15\/3 = 5<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = -15<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 12\" width=\"225\" height=\"219\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nslope m = 3\/2 y-intercept b = -2<br \/>\nm = 3\/2<br \/>\nb = -2<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (1 \u2013 (-2))\/(2 \u2013 0) = 3\/2<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = -2<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 13\" width=\"220\" height=\"235\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nm = ____________<br \/>\nb = ____________<\/p>\n<p>Answer:<br \/>\nslope m = -3 y-intercept b = 9<br \/>\nm = -3<br \/>\nb = 9<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, 9)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (9 \u2013 0))\/(0 \u2013 3) = -9\/3 = -3<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 9<\/p>\n<p><strong>Find the slope and y-intercept of the line represented by each table.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 14\" width=\"314\" height=\"78\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nm = ____________<br \/>\nb = ____________<\/p>\n<p>Answer:<br \/>\nslope m = 3 y-intercept b = 1<br \/>\nm = 3<br \/>\nb = 1<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (8, 25) and (x2, y2) = (6, 19)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (19 \u2013 25)\/(6 \u2013 8) = 6\/2 = 3<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 1<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 15\" width=\"334\" height=\"73\" \/><br \/>\nslope m = _____ y-intercept b = _____<br \/>\nm = ____________<br \/>\nb = ____________<\/p>\n<p>Answer:<br \/>\nslope m = -4 y-intercept b = 140<br \/>\nm = -4<br \/>\nb = 140<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (5, 120) and (x2, y2) = (15, 80)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (80 \u2013 120)\/(15 \u2013 5) = -40\/10 = -4<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 140<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 7.<br \/>\nHow can you determine the slope and the y-intercept of a line from a graph?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nChoose any two points on the line from the graph and use it to find the slope. Determine the point where the line crosses the y-axis to find the y-intercept.<\/p>\n<h3><a id=\"Determining_Slope_and_y-intercept_\u2013_Page_No._105\"><\/a>Independent Pratice &#8211; Determining Slope and y-intercept &#8211; Page No. 105<\/h3>\n<p>Question 8.<br \/>\nSome carpet cleaning costs are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 16\" width=\"317\" height=\"74\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nFind the slope using two points<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (1, 125) and (x2, y2) = (3, 225)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (225 \u2013 125)\/(3 \u2013 1) = 100\/2 = 50<br \/>\nFind the initial value when the value of x is 0<br \/>\nWork backward from x = 1 to x = 0<br \/>\n(175 &#8211; 125)\/(2 &#8211; 1) = 50\/1 = 50<br \/>\nSubtract the difference of x and y from the first point.<br \/>\nx = 1 &#8211; 1 = 0<br \/>\ny = 125 &#8211; 50 = 75<br \/>\ny intercept (b) = 75<br \/>\nThe slope\/rate of change represents the increase in the cost of cleaning the rooms for a unit increase in the number of rooms. The y-intercept shows the initial cost of carpet cleaning.<\/p>\n<p>Question 9.<br \/>\nMake Predictions<br \/>\nThe total cost to pay for parking at a state park for the day and rent a paddleboat are shown.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 17\" width=\"198\" height=\"250\" \/><br \/>\na. Find the cost to park for a day and the hourly rate to rent a paddleboat.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n$5<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (1, 17) and (x2, y2) = (2, 29)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (29 \u2013 17)\/(2 \u2013 1) = 12\/1 = 12<br \/>\nFind the initial value when the value of x is 0<br \/>\nWork backward from x = 1 to x = 0<br \/>\n(29 \u2013 17)\/(2 \u2013 1) = 12\/1 = 12<br \/>\nSubtract the difference of x and y from the first point.<br \/>\nx = 1 &#8211; 1 = 0<br \/>\ny = 17 &#8211; 12 = 5<br \/>\nThe cost to park for a day is $5.<\/p>\n<p>Question 9.<br \/>\nb. What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Explain.<br \/>\n$ _____________<\/p>\n<p>Answer:<br \/>\n$23.5<\/p>\n<p>Explanation:<br \/>\nWhen Lin paddles for 3.5hr<br \/>\nTotal Cost = 3.5(12) + 5 = 47<br \/>\nLin&#8217;s cost = 47\/2 = 23.5<\/p>\n<p>Question 10.<br \/>\nMulti-Step<br \/>\nRaymond\u2019s parents will pay for him to take sailboard lessons during the summer. He can take half-hour group lessons or half-hour private lessons. The relationship between cost and number of lessons is linear.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 18\" width=\"316\" height=\"113\" \/><br \/>\na. Find the rate of change and the initial value for the group lessons.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n$25<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (1, 55) and (x2, y2) = (2, 85)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (85 \u2013 55)\/(2 \u2013 1) = 30\/1 = 30<br \/>\nRate of change is $30 for per lesson<br \/>\nFind the initial value when the value of x is 0<br \/>\nWork backward from x = 1 to x = 0<br \/>\n(85 \u2013 55)\/(2 \u2013 1) = 30\/1 = 30<br \/>\nSubtract the difference of x and y from the first point.<br \/>\nx = 1 &#8211; 1 = 0<br \/>\ny = 55 &#8211; 30 = 25<br \/>\nThe initial value of the group lesson is $25.<\/p>\n<p>Question 10.<br \/>\nb. Find the rate of change and the initial value for the private lessons.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n$25<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (1, 75) and (x2, y2) = (2, 125)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (125 \u2013 75)\/(2 \u2013 1) = 50\/1 = 50<br \/>\nRate of change is $50 for per lesson<br \/>\nFind the initial value when the value of x is 0<br \/>\nWork backward from x = 1 to x = 0<br \/>\n(125 \u2013 75)\/(2 \u2013 1) = 50\/1 = 50<br \/>\nSubtract the difference of x and y from the first point.<br \/>\nx = 1 &#8211; 1 = 0<br \/>\ny = 75 &#8211; 50 = 25<br \/>\nThe initial value of the private lesson is $25.<\/p>\n<p>Question 10.<br \/>\nc. Compare and contrast the rates of change and the initial values.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe initial value for both types of lessons is the same. The rate of change is higher for private lessons then group lesson<\/p>\n<p>Explanation:<br \/>\nCompare the results of a and b<br \/>\nThe initial value for both types of lessons is the same. The rate of change is higher for private lessons then group lesson<\/p>\n<h3><a id=\"Determining_Slope_and_y-intercept_\u2013_Page_No._106\"><\/a>Vocabulary &#8211; Determining Slope and y-intercept &#8211; Page No. 106<\/h3>\n<p><strong>Explain why each relationship is not linear.<\/strong><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 19\" width=\"310\" height=\"70\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe rate of change is not constant, hence the relationship is not linear<\/p>\n<p>Explanation:<br \/>\nFind the rate of change using two points Slope m = (y2 -y1)\/(x2 \u2013 x1)<br \/>\n(6.5 &#8211; 4.5)\/(2 &#8211; 1) = 2<br \/>\n(8.5 &#8211; 6.5)\/(3 &#8211; 2) = 2<br \/>\n(11.5 &#8211; 8.5)\/(4 &#8211; 3) = 3<br \/>\nThe rate of change is not constant, hence the relationship is not linear<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 20\" width=\"312\" height=\"68\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe rate of change is not constant, hence the relationship is not linear<\/p>\n<p>Explanation:<br \/>\nFind the rate of change using two points Slope m = (y2 -y1)\/(x2 \u2013 x1)<br \/>\n(126 &#8211; 140)\/(5 &#8211; 3) = -7<br \/>\n(110 &#8211; 126)\/(7 &#8211; 5) = -8<br \/>\n(92 &#8211; 110)\/(9 &#8211; 7) = -9<br \/>\nThe rate of change is not constant, hence the relationship is not linear<\/p>\n<p>Question 13.<br \/>\nCommunicate Mathematical Ideas<br \/>\nDescribe the procedure you performed to derive the slope-intercept form of a linear equation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nExpress the slope m between a random point (x, y) on the line and the point (0, b) where the line crosses the y-axis. Then solve the equation for y.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nCritique Reasoning<br \/>\nYour teacher asked your class to describe a realworld situation in which a y-intercept is 100 and the slope is 5. Your partner gave the following description: My younger brother originally had 100 small building blocks, but he has lost 5 of them every month since.<br \/>\na. What mistake did your partner make?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIf the brother loses 5 blocks every month, the slope would be -5 and not 5.<\/p>\n<p>Explanation:<br \/>\nWhen the initial value is decreasing, the slope is negative.<br \/>\nIf the brother loses 5 blocks every month, the slope would be -5 and not 5.<\/p>\n<p>Question 14.<br \/>\nb. Describe a real-world situation that does match the situation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nI bought a 100 card pack and buy 5 additional cards every month.<\/p>\n<p>Explanation:<br \/>\nReal world situation<br \/>\nI bought a 100 card pack and buy 5 additional cards every month.<\/p>\n<p>Question 15.<br \/>\nJustify Reasoning<br \/>\nJohn has a job parking cars. He earns a fixed weekly salary of $300 plus a fee of $5 for each car he parks. His potential earnings for a week are shown in the graph. At what point does John begin to earn more from fees than his fixed salary? Justify your answer.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 2: Determining Slope and y-intercept img 21\" width=\"333\" height=\"201\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nAfter parking 60 cars, John&#8217;s earning become $600 double of his initial base salary of $300.<br \/>\nHence, after parking 61 cars, his earning from the fee becomes more than his fixed salary.<\/p>\n<p>Explanation:<br \/>\nHe earns the same in fees as his fixed salary for perking 300\/5 = 60<br \/>\nAfter parking 60 cars, John&#8217;s earning become $600 double of his initial base salary of $300.<br \/>\nHence, after parking 61 cars, his earning from the fee becomes more than his fixed salary.<\/p>\n<h3><a id=\"Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._110\"><\/a>Guided Practice &#8211; Graphing Linear Nonproportional Relationships Using Slope and y-intercept &#8211; Page No. 110<\/h3>\n<p><strong>Graph each equation using the slope and the y-intercept.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = \\(\\frac{1}{2}\\)x \u2212 3<br \/>\nslope = _____ y-intercept = _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 22\" width=\"261\" height=\"255\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nslope = 1\/2 y-intercept = -3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-1-300x158.png\" alt=\"Grade 8 Chapter 4 image 1\" width=\"300\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-1-300x158.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-1.png 718w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 1\/2 x &#8211; 3<br \/>\nThe y-intercept is b = -3. Plot the point that contains the y-intercept (0, -3)<br \/>\nThe slope m = 1\/2. Use the slope to find a second point. From (0, -3) count 1 unit up and 2 unit right. The new point is (2, -2)<br \/>\nDraw a line through the points<\/p>\n<p>Question 2.<br \/>\ny = \u22123x + 2<br \/>\nslope = _____ y-intercept = _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 23\" width=\"267\" height=\"253\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nslope = -3 y-intercept = 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-2-216x300.png\" alt=\"Grade 8 Chapter 4 image 2\" width=\"216\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-2-216x300.png 216w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-2.png 386w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><\/p>\n<p>Explanation:<br \/>\ny = -3x + 2<br \/>\nThe y-intercept is b = 2. Plot the point that contains the y-intercept (0, 2)<br \/>\nThe slope m = -3\/1. Use the slope to find a second point. From (0, 2) count 3 unit down and 1 unit right. The new point is (1, -1)<br \/>\nDraw a line through the points<\/p>\n<p>Question 3.<br \/>\nA friend gives you two baseball cards for your birthday. Afterward, you begin collecting them. You buy the same number of cards once each week. The equation y = 4x + 2 describes the number of cards, y, you have after x weeks.<br \/>\na. Find and interpret the slope and the y-intercept of the line that represents this situation. Graph y = 4x + 2. Include axis labels.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 24\" width=\"163\" height=\"190\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-3-300x285.png\" alt=\"Grade 8 Chapter 4 image 3\" width=\"300\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-3-300x285.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-3.png 545w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 4x + 2<br \/>\nThe y-intercept is b = 2. Plot the point that contains the y-intercept (0, 2)<br \/>\nThe slope m = 4. Use the slope to find a second point. From (0, 2) count 4 unit up and 1 unit right. The new point is (1, 6)<br \/>\nDraw a line through the points<\/p>\n<p>Question 3.<br \/>\nb. Discuss which points on the line do not make sense in this situation. Then plot three more points on the line that do make sense.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-4-297x300.png\" alt=\"Grade 8 Chapter 4 image 4\" width=\"297\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-4-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-4-image-4.png 522w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p>Explanation:<br \/>\nThe points with a negative value of x or y do not make sense as the number of cards or weeks cannot be negative.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 4.<br \/>\nWhy might someone choose to use the y-intercept and the slope to graph a line?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWhen the relationship is given in the form y = mx + b, the y-intercept (b) and the slope (m) are easily accessible and easily calculable. Therefore, it is a good practice to use them to graph the line.<\/p>\n<h3><a id=\"Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._111\"><\/a>Independent Practice &#8211; Graphing Linear Nonproportional Relationships Using Slope and y-intercept &#8211; Page No. 111<\/h3>\n<p>Question 5.<br \/>\nScience<br \/>\nA spring stretches in relation to the weight hanging from it according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the length of the spring in inches.<br \/>\na. Graph the equation. Include axis labels.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-7-300x180.png\" alt=\"grade 8 chapter 4 image 7\" width=\"300\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-7-300x180.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-7.png 659w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 0.75x + 0.25<br \/>\nSlope m = 0.75 and y-intercept = 0.25<br \/>\nPlot the point that contains the y-intercept (0, 0.25)<br \/>\nThe slope is m = 0.75\/1. Use the slope to find a second point. From (0,0.25) count 0.75 unit up and 1 unit right. The new point is (1, 1)<\/p>\n<p>Question 5.<br \/>\nb. Interpret the slope and the y-intercept of the line.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe slope represents the increase in the length of spring in inches for each increase of pound of weight. y-intercept represents the unstretched length of the spring When there is no weight attached.<\/p>\n<p>Question 5.<br \/>\nc. How long will the spring be if a 2-pound weight is hung on it? Will the length double if you double the weight? Explain<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nWhen there is a 2-pound weight hung, the length of the spring would be 1.75 inches. No, When there is a 4-pound weight hung, the length of the spring would be 3.25 inches and not 3.5 inches.<\/p>\n<p><strong>Look for a Pattern<\/strong><\/p>\n<p><strong>Identify the coordinates of four points on the line with each given slope and y-intercept.<\/strong><\/p>\n<p>Question 6.<br \/>\nslope = 5, y-intercept = -1<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(2, 9)<br \/>\n(3, 14)<\/p>\n<p>Explanation:<br \/>\nslope = 5, y-intercept = -1<br \/>\nPlot the point that contains the y-intercept (0, -1)<br \/>\nThe slope is m = 5\/1. Use the slope to find a second point. From (0, -1) count 5 unit up and 1 unit right. The new point is (1, 4)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(2, 9)<br \/>\n(3, 14)<\/p>\n<p>Question 7.<br \/>\nslope = -1, y-intercept = 8<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(2, 6)<br \/>\n(3, 5)<\/p>\n<p>Explanation:<br \/>\nslope = -1, y-intercept = 8<br \/>\nPlot the point that contains the y-intercept (0, 8)<br \/>\nThe slope is m = -1\/1. Use the slope to find a second point. From (0, 8) count 1 unit down and 1 unit right. The new point is (1, 7)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(2, 6)<br \/>\n(3, 5)<\/p>\n<p>Question 8.<br \/>\nslope = 0.2, y-intercept = 0.3<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(2, 0.7)<br \/>\n(3, 0.9)<\/p>\n<p>Explanation:<br \/>\nslope = 0.2, y-intercept = 0.3<br \/>\nPlot the point that contains the y-intercept (0, 0.3)<br \/>\nThe slope is m = 0.2\/1. Use the slope to find a second point. From (0, 0.3) count 0.2 unit up and 1 unit right. The new point is (1, 0.5)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(2, 0.7)<br \/>\n(3, 0.9)<\/p>\n<p>Question 9.<br \/>\nslope = 1.5, y-intercept = -3<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(2, 0)<br \/>\n(3, 1.5)<\/p>\n<p>Explanation:<br \/>\nslope = 1.5, y-intercept = -3<br \/>\nPlot the point that contains the y-intercept (0, -3)<br \/>\nThe slope is m = 1.5\/1. Use the slope to find a second point. From (0, -3) count 1.5 unit up and 1 unit right. The new point is (1, -1.5)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(2, 0)<br \/>\n(3, 1.5)<\/p>\n<p>Question 10.<br \/>\nslope = \u2212\\(\\frac{1}{2}\\), y-intercept = 4<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(4, 2)<br \/>\n(6, 1)<\/p>\n<p>Explanation:<br \/>\nslope = \u2212\\(\\frac{1}{2}\\), y-intercept = 4<br \/>\nPlot the point that contains the y-intercept (0, 4)<br \/>\nThe slope is m = \u2212\\(\\frac{1}{2}\\)\/1. Use the slope to find a second point. From (0, 4) count 1 unit down and 2 unit right. The new point is (2, 3)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(4, 2)<br \/>\n(6, 1)<\/p>\n<p>Question 11.<br \/>\nslope = \\(\\frac{2}{3}\\), y-intercept = -5<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n(6, -1)<br \/>\n(9, 1)<\/p>\n<p>Explanation:<br \/>\nslope = \\(\\frac{2}{3}\\), y-intercept = -5<br \/>\nPlot the point that contains the y-intercept (0, -5)<br \/>\nThe slope is m = \\(\\frac{2}{3}\\). Use the slope to find a second point. From (0, -5) count 2 unit up and 3 unit right. The new point is (3, -3)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(6, -1)<br \/>\n(9, 1)<\/p>\n<p>Question 12.<br \/>\nA music school charges a registration fee in addition to a fee per lesson. Music lessons last 0.5 hour. The equation y = 40x + 30 represents the total cost y of x lessons. Find and interpret the slope and y-intercept of the line that represents this situation. Then find four points on the line.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\ny = 40x + 30<br \/>\nSlope = 40<br \/>\ny-intercept = 30<br \/>\nThe slope represents the fee of the classes per lesson and y-intercept represents the registration fee.<br \/>\nPlot the point that contains the y-intercept (0, 30)<br \/>\nThe slope is m = 40\/1. Use the slope to find a second point. From (0, 30) count 40 unit up and 1 unit right. The new point is (1, 70)<br \/>\nFollow the same procedure to find the remaining three points.<br \/>\n(2, 110)<br \/>\n(3, 150)<\/p>\n<h3><a id=\"Graphing_Linear_Nonproportional_Relationships_Using_Slope_and_y-intercept_\u2013_Page_No._112\"><\/a>Graphing Linear Nonproportional Relationships Using Slope and y-intercept &#8211; Page No. 112<\/h3>\n<p>Question 13.<br \/>\nA public pool charges a membership fee and a fee for each visit. The equation y = 3x + 50 represents the cost y for x visits.<br \/>\na. After locating the y-intercept on the coordinate plane shown, can you move up three gridlines and right one gridline to find a second point? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 25\" width=\"194\" height=\"196\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nYes; Since the horizontal and vertical gridlines each represents 25 units, hence moving up 3 gridlines and right 1 gridline represent a slope a 75\/25 or 3<\/p>\n<p>Question 13.<br \/>\nb. Graph the equation y = 3x + 50. Include axis labels. Then interpret the slope and y-intercept.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-8-300x185.png\" alt=\"grade 8 chapter 4 image 8\" width=\"300\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-8-300x185.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-8.png 652w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe slope represents the fee per visit and the y-intercept represents the membership fee.<\/p>\n<p>Explanation:<br \/>\nSlope = 3<br \/>\ny-intercept = 50<br \/>\nThe slope represents the fee of the classes per lesson and the y-intercept represents the registration fee.<br \/>\nPlot the point that contains the y-intercept (0, 50)<br \/>\nThe slope is m = 3\/1. Use the slope to find a second point. From (0, 50) count 3 unit up and 1 unit right. The new point is (1, 53)<\/p>\n<p>Question 13.<br \/>\nc. How many visits to the pool can a member get for $200?<br \/>\n______ visits<\/p>\n<p>Answer:<br \/>\n50 visits<\/p>\n<p>Explanation:<br \/>\nYou would get 50 visits for $200<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-9-300x87.png\" alt=\"grade 8 chapter 4 image 9\" width=\"300\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-9-300x87.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-9-768x223.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-9.png 776w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nExplain the Error<br \/>\nA student says that the slope of the line for the equation y = 20 \u2212 15x is 20 and the y-intercept is 15. Find and correct the error.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe slope is -15 as it represents the change in y per unit change in x. The y-intercept is 20, when x = 0.<\/p>\n<p>Explanation:<br \/>\ny = 20 \u2212 15x<br \/>\nThe slope is -15 as it represents the change in y per unit change in x. The y-intercept is 20, when x = 0.<\/p>\n<p>Question 15.<br \/>\nCritical Thinking<br \/>\nSuppose you know the slope of a linear relationship and a point that its graph passes through. Can you graph the line even if the point provided does not represent the y-intercept? Explain.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYes. You can plot the given point and use the slope to find a second point. Connect the points by drawing a line.<\/p>\n<p>Question 16.<br \/>\nMake a Conjecture<br \/>\nGraph the lines y = 3x, y = 3x \u2212 3, and y = 3x + 3. What do you notice about the lines? Make a conjecture based on your observation.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 3: Graphing Linear Nonproportional Relationships Using Slope and y-intercept img 26\" width=\"231\" height=\"222\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-10-300x217.png\" alt=\"grade 8 chapter 4 image 10\" width=\"300\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-10-300x217.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-10.png 500w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nlet&#8217;s tale the example<br \/>\ny = 3x<br \/>\ny = 3x &#8211; 3<br \/>\ny = 3x + 3<br \/>\nWe notice that the lines are parallel to each other: the slopes of the lines are equal but the y-intersection point differs.<\/p>\n<h3><a id=\"Proportional_and_Nonproportional_Situations_\u2013_Page_No._117\"><\/a>Guided Practice &#8211; Proportional and Nonproportional Situations &#8211; Page No. 117<\/h3>\n<p><strong>Determine if each relationship is a proportional or nonproportional situation. Explain your reasoning.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 27\" width=\"207\" height=\"186\" \/><br \/>\nLook at the origin.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nProportional relationship<\/p>\n<p>Explanation:<br \/>\nProportional relationship<br \/>\nThe graph passes through the origin. Graph of a proportional relationship must pass through the origin<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 28\" width=\"190\" height=\"184\" \/><br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNon-proportional relationship<\/p>\n<p>Explanation:<br \/>\nThe graph does not pass through the origin. Graph of a proportional relationship must pass through the origin<br \/>\nNon-proportional relationship<\/p>\n<p>Question 3.<br \/>\nq = 2p + \\(\\frac{1}{2}\\)<br \/>\nCompare the equation with y = mx + b.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nq = 2p + \\(\\frac{1}{2}\\)<br \/>\nThe equation is in the form y = mx + b, with p being used es the variable instead of x and q instead of y. The value of m is 2, and the value b is 1\/2. Since b is not 0, the relationship presented through the above equation is non-proportional.<\/p>\n<p>Question 4.<br \/>\nv = \\(\\frac{1}{10}\\)u<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nProportional relationship<\/p>\n<p>Explanation:<br \/>\nv = \\(\\frac{1}{10}\\)u<br \/>\nCompare with the form of equation y = mx + b. The equation represent proportional relationship if b = 0<br \/>\nProportional relationship<\/p>\n<h3><a id=\"Proportional_and_Nonproportional_Situations_\u2013_Page_No._118\"><\/a>Proportional and Nonproportional Situations &#8211; Page No. 118<\/h3>\n<p><strong>The tables represent linear relationships. Determine if each relationship is a proportional or nonproportional situation.<\/strong><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 29\" width=\"200\" height=\"135\" \/><br \/>\nFind the quotient of y and x.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nproportional relationship<\/p>\n<p>Explanation:<br \/>\nFind the ratio y\/x<br \/>\n12\/3 = 4<br \/>\n36\/9 = 4<br \/>\n84\/21 = 4<br \/>\nSince the ratio is constant, the relationship is proportional.<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 30\" width=\"205\" height=\"131\" \/><br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nnon-proportional<\/p>\n<p>Explanation:<br \/>\nFind the ratio y\/x<br \/>\n4\/22 = 2\/11<br \/>\n8\/46 = 4\/23<br \/>\n10\/58 = 5\/29<br \/>\nSince the ratio is not constant, the relationship is non-proportional.<\/p>\n<p>Question 7.<br \/>\nThe values in the table represent the numbers of households that watched three TV shows and the ratings of the shows. The relationship is linear. Describe the relationship in other ways.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-31.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 31\" width=\"371\" height=\"170\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nproportional relationship<\/p>\n<p>Explanation:<br \/>\nFind the ratio y\/x<br \/>\n12\/15,000,000 = 0.0000008<br \/>\n16\/20,000,000 = 0.0000008<br \/>\n20\/25,000,000 = 0.0000008<br \/>\nSince the ratio is constant, the relationship is proportional.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 8.<br \/>\nHow are using graphs, equations, and tables similar when distinguishing between proportional and nonproportional linear relationships?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe ratio between y to x is constant when the relationship is proportional. Graphs, tables, and equations all can be used to find the ratio. The ratio is not constant when the relationship is non-proportional.<\/p>\n<h3><a id=\"Proportional_and_Nonproportional_Situations_\u2013_Page_No._119\"><\/a>Independent Practice &#8211; Proportional and Nonproportional Situations &#8211; Page No. 119<\/h3>\n<p>Question 9.<br \/>\nThe graph shows the weight of a cross-country team\u2019s beverage cooler based on how much sports drink it contains.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-32.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 32\" width=\"205\" height=\"210\" \/><br \/>\na. Is the relationship proportional or nonproportional? Explain.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNon-proportional<\/p>\n<p>Explanation:<br \/>\nThe graph does not pass through the origin. Graph of a proportional relationship must pass through the origin<br \/>\nNon-proportional<\/p>\n<p>Question 9.<br \/>\nb. Identify and interpret the slope and the y-intercept.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (12 &#8211; 10)\/(4 \u2013 0) = 0.5<br \/>\ny-intercept is the weight of the empty cooler, which is 10 lbs.<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, 10) and (x2, y2) = (4, 12)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (12 &#8211; 10)\/(4 \u2013 0) = 0.5<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 10<br \/>\ny-intercept is the weight of the empty cooler, which is 10 lbs.<\/p>\n<p><strong>In 10\u201311, tell if the relationship between a rider\u2019s height above the first floor and the time since the rider stepped on the elevator or escalator is proportional or nonproportional. Explain your reasoning.<\/strong><\/p>\n<p>Question 10.<br \/>\nThe elevator paused for 10 seconds after you stepped on before beginning to rise at a constant rate of 8 feet per second.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-33.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 33\" width=\"327\" height=\"240\" \/><br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNon-proportional<\/p>\n<p>Explanation:<br \/>\nAs there is a pause of 10 seconds, it would be the y-intercept of the graph (when x = 0)<br \/>\nNon-proportional<\/p>\n<p>Question 11.<br \/>\nYour height, h, in feet above the first floor on the escalator is given by h = 0.75t, where t is the time in seconds.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nProportional<\/p>\n<p>Explanation:<br \/>\nComparing with y = mx + b, where b = 0<br \/>\nProportional<\/p>\n<p><strong>Analyze Relationships<\/strong><\/p>\n<p><strong>Compare and contrast the two graphs.<\/strong><\/p>\n<p>Question 12.<br \/>\nGraph A\u00a0 \u00a0 \u00a0 \u00a0Graph B<br \/>\ny = \\(\\frac{1}{3}\\) x\u00a0 \u00a0 \u00a0 \u00a0 y = \\(\\sqrt { x } \\)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-34.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 34\" width=\"182\" height=\"185\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-35.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 35\" width=\"186\" height=\"192\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nGraph A represents a linear relationship while Graph B represents an exponential relationship. They both pass through the origin and the value of y increases with an increase in x.<\/p>\n<h3><a id=\"Proportional_and_Nonproportional_Situations_\u2013_Page_No._120\"><\/a>Proportional and Nonproportional Situations &#8211; Page No. 120<\/h3>\n<p>Question 13.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe a real-world situation where the relationship is linear and nonproportional.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe entrance fee to the amusement park is $8 and there is a fee of $2 per ride.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nMathematical Reasoning<br \/>\nSuppose you know the slope of a linear relationship and one of the points that its graph passes through. How can you determine if the relationship is proportional or nonproportional?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nUse the graph and the given point to determine the second point. Connect the two points by a straight line. If the graph passes through the origin, the relationship is proportional and if the graph does not pass through the origin, the relationship is non-proportional.<\/p>\n<p>Question 15.<br \/>\nMultiple Representations<br \/>\nAn entrant at a science fair has included information about temperature conversion in various forms, as shown. The variables F, C, and K represent temperatures in degrees Fahrenheit, degrees Celsius, and kelvin, respectively.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-36.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Lesson 4: Proportional and Nonproportional Situations img 36\" width=\"292\" height=\"170\" \/><br \/>\na. Is the relationship between kelvins and degrees Celsius proportional? Justify your answer in two different ways.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNo, the relationship is not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the equation B to the form: y = mx + b. Since b is not equal to 0, the relationship is non-proportional.<br \/>\nFind the ratio between the Kelvin and Degrees Celsius. Since the ration is not constant, the relationship is non-proportional.<br \/>\n281.15\/8 = 35.14<br \/>\n288.15\/15 = 19.21<br \/>\n309.15\/36 = 8.59<br \/>\nNo, the relationship is not proportional.<\/p>\n<p>Question 15.<br \/>\nb. Is the relationship between degrees Celsius and degrees Fahrenheit proportional? Why or why not?<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nNo, the relationship is not proportional.<\/p>\n<p>Explanation:<br \/>\nCompare the equation A to the form: y = mx + b. Since b is not equal to 0, the relationship is non-proportional.<br \/>\nNo, the relationship is not proportional.<\/p>\n<h3><a id=\"Representing_Linear_Nonproportional_Relationships_\u2013_Model_Quiz_\u2013_Page_No._121\"><\/a>4.1 Representing Linear Nonproportional Relationships &#8211; Model Quiz &#8211; Page No. 121<\/h3>\n<p>Question 1.<br \/>\nComplete the table using the equation y = 3x + 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-37.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 37\" width=\"277\" height=\"80\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11-300x41.png\" alt=\"grade 8 chapter 4 image 11\" width=\"300\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11-300x41.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11.png 506w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nGiven y = 3x + 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11-300x41.png\" alt=\"grade 8 chapter 4 image 11\" width=\"300\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11-300x41.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-11.png 506w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nx = -1; y = 3(-1) + 2 = -3 + 2 = -1<br \/>\nx = 0; y = 3(0) +2 = 2<br \/>\nx = 1; y = 3(1) + 2 = 3 + 2 = 5<br \/>\nx = 2; y = 3(2) + 2 = 6 + 2 = 8<br \/>\nx = 3: y = 3(3) + 2 = 9 + 2 = 11<\/p>\n<p><strong>4.2 Determining Slope and y-intercept<\/strong><\/p>\n<p>Question 2.<br \/>\nFind the slope and y-intercept of the line in the graph.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-38.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 38\" width=\"174\" height=\"151\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSlope = 3<br \/>\ny-intercept (b) = 1<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, 1) and (x2, y2) = (1, 4)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (4 &#8211; 1)\/(1 \u2013 0) = 3\/1<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = 1<\/p>\n<p><strong>4.3 Graphing Linear Nonproportional Relationships<\/strong><\/p>\n<p>Question 3.<br \/>\nGraph the equation y = 2x \u2212 3 using slope and y-intercept.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-39.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 39\" width=\"169\" height=\"159\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-12-243x300.png\" alt=\"grade 8 chapter 4 image 12\" width=\"243\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-12-243x300.png 243w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-4-image-12.png 370w\" sizes=\"(max-width: 243px) 100vw, 243px\" \/><\/p>\n<p>Explanation:<br \/>\nSlope = 2<br \/>\ny-intercept = -3<br \/>\nPlot the point that contains the y-intercept (0, -3)<br \/>\nThe slope is m = 2\/1. Use the slope to find a second point. From (0, -3) count 2 unit up and 1 unit right. The new point is (1, -1)<br \/>\nDraw a line through the points<\/p>\n<p><strong>4.4 Proportional and Nonproportional Situations<\/strong><\/p>\n<p>Question 4.<br \/>\nDoes the table represent a proportional or a nonproportional linear relationship?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-40.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Model Quiz img 40\" width=\"275\" height=\"66\" \/><br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSince the ratio is constant, the table represents a proportional linear relationship.<\/p>\n<p>Explanation:<br \/>\nFind the ratio y\/x<br \/>\n4\/1 = 4<br \/>\n8\/2 = 4<br \/>\n12\/3 = 4<br \/>\n16\/4 = 4<br \/>\n20\/5 = 4<br \/>\nSince the ratio is constant, the table represents a proportional linear relationship.<\/p>\n<p>Question 5.<br \/>\nDoes the graph in Exercise 2 represent a proportional or a nonproportional linear relationship?<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p>Explanation:<br \/>\nThe line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin.<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p>Question 6.<br \/>\nDoes the graph in Exercise 3 represent a proportional or a nonproportional relationship?<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p>Explanation:<br \/>\nThe line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 7.<br \/>\nHow can you identify a linear nonproportional relationship from a table, a graph, and an equation?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIn a table, the ratio of y\/x is not constant for non-proportional relationship.<br \/>\nIn a graph, the line of the graph does not pass through the origin for non-proportional relationship.<br \/>\nIn an equation, the b is not equal to for y = mx +b for non-proportional relationship.<\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._122\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 122<\/h3>\n<p>Question 1.<br \/>\nThe table below represents which equation?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-41.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 41\" width=\"227\" height=\"72\" \/><br \/>\nOptions:<br \/>\na. y = \u2212x \u2212 10<br \/>\nb. y = \u22126x<br \/>\nc. y = \u22124x \u2212 6<br \/>\nd. y = \u22124x + 2<\/p>\n<p>Answer:<br \/>\nc. y = \u22124x \u2212 6<\/p>\n<p>Explanation:<br \/>\nFrom the table, you can see that the y-intercept (when x = 0) is b = -6. Comparable to y = mx + b<br \/>\nThe table is represented by Option C y = -4x &#8211; 6<\/p>\n<p>Question 2.<br \/>\nThe graph of which equation is shown below?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-42.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 42\" width=\"279\" height=\"254\" \/><br \/>\nOptions:<br \/>\na. y = \u22122x + 3<br \/>\nb. y = \u22122x + 1.5<br \/>\nc. y = 2x + 3<br \/>\nd. y = 2x + 1.5<\/p>\n<p>Answer:<br \/>\na. y = \u22122x + 3<\/p>\n<p>Explanation:<br \/>\nFrom the table, you can see that the y-intercept (when x = 0) is b = 3. Comparable to y = mx + b<br \/>\nThe Option B and D are rejected.<br \/>\nSince the graph is slanting downwards, the slope is negative.<br \/>\nOption C is rejected<br \/>\nThe graph represents y = -2x + 3<\/p>\n<p>Question 3.<br \/>\nThe table below represents a linear relationship.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-43.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 43\" width=\"231\" height=\"77\" \/><br \/>\nWhat is the y-intercept?<br \/>\nOptions:<br \/>\na. -4<br \/>\nb. -2<br \/>\nc. 2<br \/>\nd. 3<\/p>\n<p>Answer:<br \/>\nb. -2<\/p>\n<p>Explanation:<br \/>\nFind the rate of change<br \/>\n(7 &#8211; 4)\/(3 &#8211; 2) = (10 &#8211; 7)\/(4 &#8211; 3) = 3<br \/>\nFind the value of y for x = 0<br \/>\nWorks backward from x = 2 to x = 1<br \/>\nx = 2 &#8211; 1 = 1<br \/>\ny = 4 &#8211; 3 = 1<br \/>\nx = 1 &#8211; 1 = 0<br \/>\ny = 1 &#8211; 3 = -2<br \/>\ny intercept = -2<\/p>\n<p>Question 4.<br \/>\nWhich equation represents a nonproportional relationship?<br \/>\nOptions:<br \/>\na. y = 3x + 0<br \/>\nb. y = \u22123x<br \/>\nc. y = 3x + 5<br \/>\nd. y = \\(\\frac{1}{3}\\)x<\/p>\n<p>Answer:<br \/>\nc. y = 3x + 5<\/p>\n<p>Explanation:<br \/>\nFor a non-proportional relationship, the equation is y = mx + b and b is not equal to 0.<br \/>\nOption C represents a non-proportional relationship y = 3x + 5<\/p>\n<p>Question 5.<br \/>\nThe table shows a proportional relationship. What is the missing y-value?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-44.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 44\" width=\"209\" height=\"73\" \/><br \/>\nOptions:<br \/>\na. 16<br \/>\nb. 20<br \/>\nc. 18<br \/>\nd. 24<\/p>\n<p>Answer:<br \/>\nc. 18<\/p>\n<p>Explanation:<br \/>\nFind the ratio y\/x<br \/>\n6\/4 = 3\/2<br \/>\nSince the relationship is proportional, the ratio is constant.<br \/>\nUsing the ratio to fins missing y<br \/>\n3\/2 = y\/12<br \/>\ny = 3\/2 \u00d7 12 = 18<\/p>\n<p>Question 6.<br \/>\nWhat is 0.00000598 written in scientific notation?<br \/>\nOptions:<br \/>\na. 5.98 \u00d7 10<sup>-6<\/sup><br \/>\nb. 5.98 \u00d7 10<sup>-5<\/sup><br \/>\nc. 59.8 \u00d7 10<sup>-6<\/sup><br \/>\nd. 59.8 \u00d7 10<sup>-7<\/sup><\/p>\n<p>Answer:<br \/>\nc. 59.8 \u00d7 10<sup>-6<\/sup><\/p>\n<p>Explanation:<br \/>\n0.00000598<br \/>\nMove the decimal 6 points<br \/>\n59.8 \u00d7 10<sup>-6<\/sup><\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 7.<br \/>\nThe graph shows a linear relationship.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-4-Nonproportional-Relationships-img-45.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships Mixed Review img 45\" width=\"283\" height=\"254\" \/><br \/>\na. Is the relationship proportional or nonproportional?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p>Explanation:<br \/>\nThe line of the graph does not pass through the origin. The graph of a proportional relationship must pass through the origin.<br \/>\nIt represents a non-proportional linear relationship<\/p>\n<p>Question 7.<br \/>\nb. What is the slope of the line?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nSlope m = -2<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (-3 -1)\/(0 + 2) = -4\/2 = -2<\/p>\n<p>Question 7.<br \/>\nc. What is the y-intercept of the line?<br \/>\n_______<\/p>\n<p>Answer:<br \/>\ny-intercept (b) = -3<\/p>\n<p>Explanation:<br \/>\nFrom the graph when x = 0<br \/>\ny-intercept (b) = -3<\/p>\n<p>Question 7.<br \/>\nd. What is the equation of the line?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -2x &#8211; 3<\/p>\n<p>Explanation:<br \/>\nSubstitute m and b in the form: y = mx + b<br \/>\ny = -2x &#8211; 3<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>I believe that our Go Math Grade 8 Answer Key Chapter 4 Nonproportional Relationships pdf brought a smile to your face. All the beginners can easily start their practice with our step by step explanations. Bookmark our ccssmathanswers.com to get the latest information about the solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Are you searching for Go Math 8th Grade Answer Key Chapter 4 Nonproportional Relationships? If yes, then download Go Math Grade 8 Answer Key pdf from here in this article. It helps the students to score good marks in the exams. 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