{"id":6379,"date":"2022-03-27T15:19:10","date_gmt":"2022-03-27T09:49:10","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6379"},"modified":"2022-04-07T12:49:54","modified_gmt":"2022-04-07T07:19:54","slug":"go-math-grade-8-answer-key-chapter-3-proportional-relationships","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-3-proportional-relationships\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships"},"content":{"rendered":"<p>Who doesn\u2019t love the best learning? HMH Grade 8 Go Math Answer Key Chapter 3 Proportional Relationships is the perfect guide for students who love maths. Pupils can habituate practice maths if they start their practice with Go Math 8th Grade Chapter 3 Proportional Relationships Solution Key. The <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> includes an explanation for all the questions where students can easily understand the methods in an easy manner.<\/p>\n<h2>Go Math Grade 8 Chapter 3 Proportional Relationships Answer Key<\/h2>\n<p>Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships offers the best way to practice math with simple techniques. The students can download and practice the questions from Go Math Grade 8 Text Book for free. The HMH Go Math Grade 8 Answer Key is provided will help the students to score the highest marks in the exams.<\/p>\n<p><strong>Lesson 1: Representing Proportional Relationships<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Representing_Proportional_Relationships_\u2013_Page_No._74\">\u00b7 Representing Proportional Relationships \u2013 Page No. 74<\/a><\/li>\n<li><a href=\"#\u00b7_Representing_Proportional_Relationships_\u2013_Page_No._75\">\u00b7 Representing Proportional Relationships \u2013 Page No. 75<\/a><\/li>\n<li><a href=\"#\u00b7_Representing_Proportional_Relationships_Lesson_Check_\u2013_Page_No._76\">\u00b7 Representing Proportional Relationships Lesson Check \u2013 Page No. 76<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Rate of Change and Slope<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Rate_of_Change_and_Slope_\u2013_Page_No._80\">\u00b7 Rate of Change and Slope \u2013 Page No. 80<\/a><\/li>\n<li><a href=\"#\u00b7_Rate_of_Change_and_Slope_\u2013_Page_No._81\">\u00b7 Rate of Change and Slope \u2013 Page No. 81<\/a><\/li>\n<li><a href=\"#\u00b7_Rate_of_Change_and_Slope_Lesson_Check_\u2013_Page_No._82\">\u00b7 Rate of Change and Slope Lesson Check \u2013 Page No. 82<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Interpreting the Unit As Slope<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Interpreting_the_Unit_As_Slope_\u2013_Page_No._86\">\u00b7 Interpreting the Unit As Slope \u2013 Page No. 86<\/a><\/li>\n<li><a href=\"#\u00b7_Interpreting_the_Unit_As_Slope_\u2013_Page_No._87\">\u00b7 Interpreting the Unit As Slope \u2013 Page No. 87<\/a><\/li>\n<li><a href=\"#\u00b7_Interpreting_the_Unit_As_Slope_Lesson_Check_\u2013_Page_No._88\">\u00b7 Interpreting the Unit As Slope Lesson Check \u2013 Page No. 88<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Representing Proportional Relationships \u2013 Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Representing_Proportional_Relationships_\u2013_Model_Quiz_\u2013_Page_No._89\">\u00b7 Representing Proportional Relationships \u2013 Model Quiz \u2013 Page No. 89<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Mixed_Review_\u2013_Page_No._90\">Mixed Review \u2013 Page No. 90<\/a><\/li>\n<\/ul>\n<h3><a id=\"\u00b7_Representing_Proportional_Relationships_\u2013_Page_No._74\"><\/a>Guided Practice &#8211; Representing Proportional Relationships &#8211; Page No. 74<\/h3>\n<p>Question 1.<br \/>\nVocabulary<br \/>\nA proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity <span style=\"text-decoration: underline;\">is\/is not<\/span> constant.<br \/>\n______ constant<\/p>\n<p>Answer:<br \/>\nis constant<\/p>\n<p>Explanation:<br \/>\nThe rent would be proportional so therefore it is.<\/p>\n<p>Question 2.<br \/>\nVocabulary<br \/>\nWhen writing an equation of a proportional relationship in the form y = kx, k represents the __________________________.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nconstant of proportionality<\/p>\n<p>Explanation:<br \/>\nWhen writing an equation of a proportional relationship in the form y = kx, k represents the constant of proportionality.<\/p>\n<p>Question 3.<br \/>\nWrite an equation that describes the proportional relationship between the number of days and the number of weeks in a given length of time.<br \/>\na. Complete the table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 1\" width=\"497\" height=\"85\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-1-300x47.jpg\" alt=\"Grade 8 Chapter 3 image 1\" width=\"332\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-1-300x47.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-1.jpg 669w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 3.<br \/>\nb. Let x represent _____.<br \/>\nLet y represent _____.<br \/>\nThe equation that describes the relationship is _____.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nLet x represent the time in weeks.<br \/>\nLet y represent the time in days.<br \/>\nThe equation that describes the relationship is y = 7x.<\/p>\n<p><strong>Each table or graph represents a proportional relationship. Write an equation that describes the relationship.<\/strong><\/p>\n<p>Question 4.<br \/>\nPhysical Science<br \/>\nThe relationship between the numbers of oxygen atoms and hydrogen atoms in water.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 2\" width=\"338\" height=\"108\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = 2x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-2-300x89.jpg\" alt=\"Grade 8 Chapter 3 image 2\" width=\"300\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-2-300x89.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-2.jpg 452w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nx represents the Oxygen atoms<br \/>\ny represents the Hydrogen atoms<br \/>\nFor every point of the x-axis, the y-axis is varying with 2x times.<br \/>\ny = 2x<\/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-3-Proportional-Relationships-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 3\" width=\"221\" height=\"207\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = 30x<\/p>\n<p>Explanation:<br \/>\nx represents the Distance in inches<br \/>\ny represents the Actual Distance in miles<br \/>\nFor every point of the x-axis, the y-axis is varying with 30x times.<br \/>\ny = 30x<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nIf you know the equation of a proportional relationship, how can you draw the graph of the equation?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nUse the equation to make a table with x-values and y-values. Then graph the points (x, y) and draw a line through the points.<\/p>\n<h3><a id=\"\u00b7_Representing_Proportional_Relationships_\u2013_Page_No._75\"><\/a>Independent Practice &#8211; Representing Proportional Relationships &#8211; Page No. 75<\/h3>\n<p><strong>The table shows the relationship between temperatures measured on the Celsius and Fahrenheit scales.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 4\" width=\"528\" height=\"75\" \/><\/p>\n<p>Question 7.<br \/>\nIs the relationship between the temperature scales proportional? Why or why not?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNo. The ratios of the numbers in each column are not equal.<\/p>\n<p>Explanation:<br \/>\nFahrenheit Temperature\/Celsius Temperature = 50\/10 = 5<br \/>\n86\/30 = 2.87<br \/>\n122\/50 = 2.44<br \/>\nThe relationship is not propotional as the ratio is not constant.<\/p>\n<p>Question 8.<br \/>\nDescribe the graph of the Celsius-Fahrenheit relationship.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nA line starting at (0, 32) and slanting upward to the right.<\/p>\n<p>Explanation:<br \/>\nThe graph is a straight line with a y-intercept of 32.<\/p>\n<p>Question 9.<br \/>\nAnalyze Relationships<br \/>\nRalph opened a savings account with a deposit of $100. Every month after that, he deposited $20 more.<br \/>\na. Why is the relationship described not proportional?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe account had a balance of $100, to begin with.<\/p>\n<p>Question 9.<br \/>\nb. How could the situation be changed to make the situation proportional?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nHave Ralph open the account with no money, to begin with, and then put $20 every month.<\/p>\n<p>Question 10.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe a real-world situation that can be modeled by the equation y = \\(\\frac{1}{20}\\)x. Be sure to describe what each variable represents.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nIf x is the number of nickels you have, y = \\(\\frac{1}{20}\\)x is the amount of money you have in dollars.<\/p>\n<p><strong>Look for a Pattern<\/strong><\/p>\n<p><strong>The variables x and y are related proportionally.<\/strong><\/p>\n<p>Question 11.<br \/>\nWhen x = 8, y = 20. Find y when x = 42.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\ny = 105<\/p>\n<p>Explanation:<br \/>\nx = 8, y = 20<br \/>\ny\/x = 20\/8<br \/>\ny = 20x\/8<br \/>\nwhen x = 42<br \/>\ny = (20 \u00d7 42)\/8<br \/>\ny = 105<\/p>\n<p>Question 12.<br \/>\nWhen x = 12, y = 8. Find x when y = 12.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nx = 18<\/p>\n<p>Explanation:<br \/>\nx\/y = 12\/8<br \/>\nx = 12y\/8<br \/>\nwhen y = 12<br \/>\nx = (12 \u00d7 12)\/8<br \/>\nx = 18<\/p>\n<h3><a id=\"\u00b7_Representing_Proportional_Relationships_Lesson_Check_\u2013_Page_No._76\"><\/a>Representing Proportional Relationships &#8211; Page No. 76<\/h3>\n<p>Question 13.<br \/>\nThe graph shows the relationship between the distance that a snail crawls and the time that it crawls.<br \/>\na. Use the points on the graph to make a table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 5\" width=\"466\" height=\"77\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 6\" width=\"211\" height=\"229\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10-300x41.png\" alt=\"Grade 8 Chapter 3 image 10\" width=\"300\" height=\"41\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10-300x41.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10.png 491w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 13.<br \/>\nb. Write the equation for the relationship and tell what each variable represents.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = 1\/10 x, where y is the time in minutes and x is the distance in inches<\/p>\n<p>Question 13.<br \/>\nc. How long does it take the snail to crawl 85 inches?<br \/>\n_______ minutes<\/p>\n<p>Answer:<br \/>\n8.5 minutes<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nCommunicate Mathematical Ideas<br \/>\nExplain why all of the graphs in this lesson show the first quadrant but omit the other three quadrants.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nAll of the graphs represent real-world data for which both x and y take on only nonnegative values, which graph in the first quadrant or on the axes. If either x or y or both could be negative, then other quadrants would be needed.<\/p>\n<p>Question 15.<br \/>\nAnalyze Relationships<br \/>\nComplete the table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 1: Representing Proportional Relationships img 7\" width=\"545\" height=\"107\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-medium wp-image-7771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10-1-300x45.png\" alt=\"Grade 8 Chapter 3 image 10\" width=\"300\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10-1-300x45.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-10-1.png 655w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\na. Are the length of a side of a square and the perimeter of the square related proportionally? Why or why not?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nYes. The ratio of the perimeter of a square to its side length is always 4.<\/p>\n<p>Question 15.<br \/>\nb. Are the length of a side of a square and the area of the square related proportionally? Why or why not?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nNo. The ratio of the area of a square to its side length is not constant<\/p>\n<p>Question 16.<br \/>\nMake a Conjecture<br \/>\nA table shows a proportional relationship where k is the constant of proportionality. The rows are then switched. How does the new constant of proportionality relate to the original one?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nIt is the reciprocal of the original constant of proportionality<\/p>\n<h3><a id=\"\u00b7_Rate_of_Change_and_Slope_\u2013_Page_No._80\"><\/a>Guided Practice &#8211; Rate of Change and Slope &#8211; Page No. 80<\/h3>\n<p><strong>Tell whether the rates of change are constant or variable.<\/strong><\/p>\n<p>Question 1.<br \/>\nbuilding measurements _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 8\" width=\"335\" height=\"77\" \/><br \/>\n______________<\/p>\n<p>Answer:<br \/>\nconstant<\/p>\n<p>Explanation:<br \/>\nInput variable: Feet<br \/>\nOutput variable: Yard<br \/>\nFor every point of the Yard, the Feet is increasing 3 times.<br \/>\nSo, the answer is constant.<\/p>\n<p>Question 2.<br \/>\ncomputers sold _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 9\" width=\"331\" height=\"72\" \/><br \/>\n______________<\/p>\n<p>Answer:<br \/>\nvariable<\/p>\n<p>Explanation:<br \/>\nIdentify the input and output variables<br \/>\nInput variable: Week<br \/>\nOutput variable: The number sold<br \/>\nx-axis and y-axis points are not varying constantly. So, the answer is variable.<\/p>\n<p>Question 3.<br \/>\ndistance an object falls _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 10\" width=\"340\" height=\"73\" \/><br \/>\n______________<\/p>\n<p>Answer:<br \/>\nvariable<\/p>\n<p>Explanation:<br \/>\nIdentify the input and output variables<br \/>\nInput variable: Time<br \/>\nOutput variable: Distance<br \/>\nx-axis and y-axis points are not varying constantly. So, the answer is variable.<\/p>\n<p>Question 4.<br \/>\ncost of sweaters _____<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 11\" width=\"329\" height=\"64\" \/><br \/>\n______________<\/p>\n<p>Answer:<br \/>\nconstant<\/p>\n<p>Explanation:<br \/>\nIdentify the input and output variables<br \/>\nInput variable: Number<br \/>\nOutput variable: Cost<br \/>\nx-axis and y-axis points are varying constantly. So, the answer is constant.<\/p>\n<p><strong>Erica walks to her friend Philip\u2019s house. The graph shows Erica\u2019s distance from home over time.<\/strong><\/p>\n<p>Question 5.<br \/>\nFind the rate of change from 1 minute to 2 minutes.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 12\" width=\"164\" height=\"186\" \/><br \/>\n\\(\\frac{\\text { change in distance }}{\\text { change in time }}=\\frac{400-?}{2-?}=\\frac{?}{?}=?\\) ft per min<br \/>\n________ feet per minute<\/p>\n<p>Answer:<br \/>\n200 feet per minute<\/p>\n<p>Explanation:<br \/>\n(400 &#8211; 200)\/(2 &#8211; 1)<br \/>\n200\/1<br \/>\n200 feet per minute<\/p>\n<p>Question 6 (request help)<br \/>\nFind the rate of change from 1 minute to 4 minutes.<br \/>\n______ feet per minute<\/p>\n<p>Answer:<br \/>\n200 ft per min<\/p>\n<p>Explanation:<br \/>\nchange in distance\/change in time<br \/>\n(800 &#8211; 200)\/(4 &#8211; 1)<br \/>\n600\/3 = 200 ft per min<\/p>\n<p><strong>Find the slope of each line.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 13\" width=\"238\" height=\"245\" \/><br \/>\nslope = _____<br \/>\n________<\/p>\n<p>Answer:<br \/>\nslope = -2<\/p>\n<p>Explanation:<br \/>\nFrom the given image, the x-axis is separated with 1 unit.<br \/>\nthe y-axis is separated with 1 unit.<br \/>\nFor every 1 unit of the x-axis, the slope is taken -2 units on the y-axis<br \/>\nThe slope of the line is -2<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 14\" width=\"240\" height=\"237\" \/><br \/>\nslope = _____<br \/>\n\\(\\frac{\u25a1}{\u25a1}\\)<\/p>\n<p>Answer:<br \/>\n\\(\\frac{3}{2}\\)<\/p>\n<p>Explanation:<br \/>\nFrom the given image, the slope is 3\/2<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 9.<br \/>\nIf you know two points on a line, how can you find the rate of change of the variables being graphed?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nFind the coordinates of two points on the line. Then divide the change in y-values from one point to the next by the change in x-values.<\/p>\n<h3><a id=\"\u00b7_Rate_of_Change_and_Slope_\u2013_Page_No._81\"><\/a>Independent Practice &#8211; Rate of Change and Slope &#8211; Page No. 81<\/h3>\n<p>Question 10.<br \/>\nRectangle EFGH is graphed on a coordinate plane with vertices at E(-3, 5), F(6, 2), G(4, -4), and H(-5, -1).<br \/>\na. Find the slopes of each side.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSlope EF = 1\/3<br \/>\nslope FG = 3<br \/>\nslope GH = -1\/3<br \/>\nslope HE =3<\/p>\n<p>Question 10.<br \/>\nb. What do you notice about the slopes of opposite sides?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThey are the same.<\/p>\n<p>Question 10.<br \/>\nc. What do you notice about the slopes of adjacent sides?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThey are negative reciprocals of one another.<\/p>\n<p>Question 11.<br \/>\nA bicyclist started riding at 8:00 A.M. The diagram below shows the distance the bicyclist had traveled at different times. What was the bicyclist\u2019s average rate of speed in miles per hour?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 15\" width=\"567\" height=\"101\" \/><br \/>\n_______ miles per hour<\/p>\n<p>Answer:<br \/>\n15 miles per hour<\/p>\n<p>Explanation:<br \/>\nTotal distance traveled by bicyclist = 4.5 mile + 7.5 mile = 12 mile<br \/>\nTotal time taken by bicyclist = (8:48 A.M &#8211; 8:00 A.M) = 48 min = 0.8 hr<br \/>\nconversion used : ( 1 hour = 60 minute)<br \/>\nAverage rate of speed = total distance\/total time = 15 mile\/hr<\/p>\n<p>Question 12.<br \/>\nMultistep<br \/>\nA line passes through (6, 3), (8, 4), and (n, -2). Find the value of n.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nn = -4<\/p>\n<p>Explanation:<br \/>\nA line passes through (6, 3), (8, 4), and (n, -2).<br \/>\nFrom the given information, for every 2 points on x-axis, the y-values are changing one point.<br \/>\n(4, 2), (2, 1), (0, 0), (-2, -1), (-4, -2)<\/p>\n<p>Question 13.<br \/>\nA large container holds 5 gallons of water. It begins leaking at a constant rate. After 10 minutes, the container has 3 gallons of water left.<br \/>\na. At what rate is the water leaking?<br \/>\n_______ gallons per minute<\/p>\n<p>Answer:<br \/>\n1 gallon every 5 minutes, or 0.2 gal\/min<\/p>\n<p>Explanation:<br \/>\nRate = (5 &#8211; 3)\/(0 &#8211; 10)<br \/>\n= 2\/-10<br \/>\n= -0.2<br \/>\nThe rate of water leaking is 1 gallon every 5 minutes, or 0.2 gal\/min<\/p>\n<p>Question 13.<br \/>\nb. After how many minutes will the container be empty?<br \/>\n_______ minutes<\/p>\n<p>Answer:<br \/>\n25 minutes<\/p>\n<p>Explanation:<br \/>\nNumber of minutes = 5\/0.2 = 25<br \/>\nIt will take 25 minutes for the container to be empty.<\/p>\n<p>Question 14.<br \/>\nCritique Reasoning<br \/>\nBilly found the slope of the line through the points (2, 5) and (-2, -5) using the equation \\(\\frac{2-(-2)}{5-(-5)}=\\frac{2}{5}\\). What mistake did he make?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nHe used the change in x over the change in y instead of the change in y over the change in x.<\/p>\n<h3><a id=\"\u00b7_Rate_of_Change_and_Slope_Lesson_Check_\u2013_Page_No._82\"><\/a>Rate of Change and Slope &#8211; Page No. 82<\/h3>\n<p>Question 15.<br \/>\nMultiple Representations<br \/>\nGraph parallelogram ABCD on a coordinate plane with vertices at A(3, 4), B(6, 1), C(0, -2), and D(-3, 1).<br \/>\na. Find the slope of each side.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 2: Rate of Change and Slope img 16\" width=\"307\" height=\"300\" \/><br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nslope AB = -1;<br \/>\nslope BC = 1\/2<br \/>\nslope CD = -1;<br \/>\nslope DA = 1\/2<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-5-300x293.jpg\" alt=\"Grade 8 Chapter 3 image 5\" width=\"276\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-5-300x293.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-5.jpg 508w\" sizes=\"(max-width: 276px) 100vw, 276px\" \/><\/p>\n<p>Question 15.<br \/>\nb. What do you notice about the slopes?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe slopes of the opposite sides are the same.<\/p>\n<p>Question 15.<br \/>\nc. Draw another parallelogram on the coordinate plane. Do the slopes have the same characteristics?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYes; opposite sides still have the same slope.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 16.<br \/>\nCommunicate Mathematical Ideas<br \/>\nBen and Phoebe are finding the slope of a line. Ben chose two points on the line and used them to find the slope. Phoebe used two different points to find the slope. Did they get the same answer? Explain.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nYes. The slope of a line is constant. Therefore, the slope that you calculate will be the same no matter which two points you choose.<\/p>\n<p>Question 17.<br \/>\nAnalyze Relationships<br \/>\nTwo lines pass through the origin. The lines have slopes that are opposites. Compare and contrast the lines.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nOne line has a positive slope and one has a negative slope. The lines are equally steep, but one slants upward left to right while the other slants downward left to right. The lines cross at the origin.<\/p>\n<p>Question 18.<br \/>\nReason Abstractly<br \/>\nWhat is the slope of the x-axis? Explain.<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nZero. The rise along the x-axis is zero, while the run along the x-axis is not zero. The slope zero\/run or zero.<\/p>\n<h3><a id=\"\u00b7_Interpreting_the_Unit_As_Slope_\u2013_Page_No._86\"><\/a>Guided Practice &#8211; Interpreting the Unit As Slope &#8211; Page No. 86<\/h3>\n<p><strong>Give the slope of the graph and the unit rate.<\/strong><\/p>\n<p>Question 1.<br \/>\nJorge: 5 miles every 6 hours<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 17\" width=\"243\" height=\"226\" \/><br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) miles per hour<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{6}\\) miles per hour<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-11.png\" alt=\"Grade 8 Chapter 3 image 11\" width=\"207\" height=\"183\" \/><br \/>\nSlope = rise\/run = 5\/6<br \/>\nThe unit rate a the distance traveled and the slope a the graph of the relationship is equal, 5\/6 miles per hour<br \/>\nCalculate miles PER hour<br \/>\n5\/6<\/p>\n<p>Question 2.<br \/>\nAkiko<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 18\" width=\"344\" height=\"295\" \/><br \/>\n\\(\\frac{\u25a1}{\u25a1}\\) miles per hour<\/p>\n<p>Answer:<br \/>\n\\(\\frac{5}{4}\\) miles per hour<\/p>\n<p>Explanation:<br \/>\nCalculate miles PER hour<br \/>\n5 miles\/4hours = 5\/4 miles per hour<\/p>\n<p>Question 3.<br \/>\nThe equation y = 0.5x represents the distance Henry hikes, in miles, over time, in hours. The graph represents the rate that Clark hikes. Determine which hiker is faster. Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 19\" width=\"202\" height=\"209\" \/><br \/>\n___________<\/p>\n<p>Answer:<br \/>\nClark is faster.<\/p>\n<p>Explanation:<br \/>\nFrom the equation, Henry\u2019s rate is equal to 0.5, or 1\/2 mile per hour. Clark\u2019s rate is the slope of the line, which is 3\/2\u00a0or 1.5 miles per hour.<\/p>\n<p><strong>Write an equation relating the variables in each table.<\/strong><\/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-3-Proportional-Relationships-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 20\" width=\"329\" height=\"77\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\ny = 15x<\/p>\n<p>Explanation:<br \/>\ny\/x = 15\/1<br \/>\ny = 15x<br \/>\nMultiply 15 with the x values to get the y values.<br \/>\ny = 15x<\/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-3-Proportional-Relationships-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 21\" width=\"325\" height=\"72\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\ny = 3\/8 x<\/p>\n<p>Explanation:<br \/>\ny\/x = 6\/16<br \/>\ny\/x = 3\/8<br \/>\ny = 3\/8 x<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nDescribe methods you can use to show a proportional relationship between two variables, x and y. For each method, explain how you can find the unit rate and the slope.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nThe ratio of y to x gives the unit rate and slope.<\/p>\n<p>Explanation:<br \/>\nIf the equation can be written as y = mx, then m is the unit rate and the slope. Graph: When the line passes through the origin, then the value of r at the point (1, r) is the unit rate and the slope.<\/p>\n<h3><a id=\"\u00b7_Interpreting_the_Unit_As_Slope_\u2013_Page_No._87\"><\/a>Independent Practice &#8211; Interpreting the Unit As Slope &#8211; Page No. 87<\/h3>\n<p>Question 7.<br \/>\nA Canadian goose migrated at a steady rate of 3 miles every 4 minutes.<br \/>\na. Fill in the table to describe the relationship.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 22\" width=\"357\" height=\"75\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-6-300x62.jpg\" alt=\"Grade 8 Chapter 3 image 6\" width=\"300\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-6-300x62.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-6.jpg 509w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nCanadian goose migrated at a steady rate of 3 miles every 4 minutes<br \/>\ny\/x = 3\/4; x\/y = 4\/3<br \/>\ny = 3\/4 x; x = 4\/3 y<br \/>\nIf x = 8, y = 3\/4 \u00d7 8 = 6<br \/>\nIf y = 9, x = 4\/3 \u00d7 9 = 12<br \/>\nIf y = 12, x = 4\/3 \u00d7 12 = 16<br \/>\nIf x = 20, y = 3\/4 \u00d7 20 = 15<\/p>\n<p>Question 7.<br \/>\nb. Graph the relationship.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 23\" width=\"281\" height=\"228\" \/><br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-7-279x300.jpg\" alt=\"Grade 8 Chapter 3 image 7\" width=\"256\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-7-279x300.jpg 279w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-7.jpg 373w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><\/p>\n<p>Explanation:<br \/>\nThe points are (4, 3), (8, 6), (12, 9), (16, 12), (20, 15)<\/p>\n<p>Question 7.<br \/>\nc. Find the slope of the graph and describe what it means in the context of this problem.<br \/>\nSlope: \\(\\frac{\u25a1}{\u25a1}\\) miles per minute<\/p>\n<p>Answer:<br \/>\nSlope: \\(\\frac{3}{4}\\) miles per minute<\/p>\n<p>Explanation:<br \/>\nThe unit rate of migration of the goose and the slope of the graph both equal 3\/4 mi\/min<\/p>\n<p>Question 8.<br \/>\nVocabulary<br \/>\nA unit rate is a rate in which the first quantity \/ second quantity in the comparison is one unit.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nsecond quantity<\/p>\n<p>Explanation:<br \/>\nA unit rate is a rate in which the &#8220;second quantity&#8221; in the comparison is one unit<\/p>\n<p>Question 9.<br \/>\nThe table and the graph represent the rate at which two machines are bottling milk in gallons per second.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 24\" width=\"606\" height=\"209\" \/><br \/>\na. Determine the slope and unit rate of each machine.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nMachine 1: slope = unit rate = 0.6\/1 = 0.6 gal\/s<br \/>\nMachine 2: slope = unit rate = 3\/4 = 0.75 gal\/s<\/p>\n<p>Question 9.<br \/>\nb. Determine which machine is working at a faster rate.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nMachine 2 is working at a faster rate since 0.75 &gt; 0.6<\/p>\n<h3><a id=\"\u00b7_Interpreting_the_Unit_As_Slope_Lesson_Check_\u2013_Page_No._88\"><\/a>Interpreting the Unit As Slope &#8211; Page No. 88<\/h3>\n<p>Question 10.<br \/>\nCycling<br \/>\nThe equation y = \\(\\frac{1}{9}\\) x represents the distance y, in kilometers, that Patrick traveled in x minutes while training for the cycling portion of a triathlon. The table shows the distance y Jennifer traveled in x minutes in her training. Who has the faster training rate?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 25\" width=\"319\" height=\"76\" \/><br \/>\n___________<\/p>\n<p>Answer:<br \/>\nJennifer has a faster training rate<\/p>\n<p>Explanation:<br \/>\nPatrick\u2019s rate is 1\/9 kilometer per minute. Jennifer\u2019s rate is 1\/8 kilometer per minute. 1\/9 &lt; 1\/8. So, Jennifer has a faster training rate.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 11.<br \/>\nAnalyze Relationships<br \/>\nThere is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 4.75). What is the slope of the graph? What is the unit rate? Explain.<br \/>\n______ dollars per minute<\/p>\n<p>Answer:<br \/>\n$4.75\/min<\/p>\n<p>Explanation:<br \/>\nslope = unit rate = 4.75.<br \/>\nIf the graph of a proportional relationship passes through the point (1, r), then r equals the slope and the unit rate, which is $4.75\/min.<\/p>\n<p>Question 12.<br \/>\nDraw Conclusions<br \/>\nTwo cars start at the same time and travel at different constant rates. A graph for Car A passes through the point (0.5, 27.5), and a graph for Car B passes through (4, 240). Both graphs show distance in miles and time in hours. Which car is traveling faster? Explain.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nCar B<\/p>\n<p>Explanation:<br \/>\nThe slope and unit rate of speed of Car A is (27.5 &#8211; 0)\/(0.5 &#8211; 0) = 27.5\/0.5 = 55 mi\/h.<br \/>\nThe slope and unit rate of speed of Car B is (240 &#8211; 0)\/(4 &#8211; 0) = 240\/4 = 60 mi\/h.<br \/>\n60 &gt; 55, so Car B is traveling faster.<\/p>\n<p>Question 13.<br \/>\nCritical Thinking<br \/>\nThe table shows the rate at which water is being pumped into a swimming pool. Use the unit rate and the amount of water pumped after 12 minutes to find how much water will have been pumped into the pool after 13 \\(\\frac{1}{2}\\) minutes. Explain your reasoning.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Lesson 3: Interpreting the Unit As Slope img 26\" width=\"291\" height=\"72\" \/><br \/>\n______ gallons<\/p>\n<p>Answer:<br \/>\n243 gallons<\/p>\n<p>Explanation:<br \/>\nThe unit rate is 36\/2 = 18gal\/min.<br \/>\nSo, 1 1\/2 minutes after 12 minutes, an additional 18 \u00d7 1 1\/2 = = 27 gallons will be pumped in.<br \/>\nSo, the total is 216 + 27 = 243 gal.<\/p>\n<h3><a id=\"\u00b7_Representing_Proportional_Relationships_\u2013_Model_Quiz_\u2013_Page_No._89\"><\/a>3.1 Representing Proportional Relationships &#8211; Model Quiz &#8211; Page No. 89<\/h3>\n<p>Question 1.<br \/>\nFind the constant of proportionality for the table of values.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Model Quiz img 27\" width=\"231\" height=\"69\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\n1.5<\/p>\n<p>Explanation:<br \/>\nconstant of proportionality<br \/>\nk = y\/x = 3\/2 = 1.5<br \/>\nk = y\/x = 4.5\/3 = 1.5<br \/>\nk = y\/x = 6\/4 = 1.5<br \/>\nk = y\/x = 7.5\/5 = 1.5<\/p>\n<p>Question 2.<br \/>\nPhil is riding his bike. He rides 25 miles in 2 hours, 37.5 miles in 3 hours, and 50 miles in 4 hours. Find the constant of proportionality and write an equation to describe the situation.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nThe constant of proportionality is 12.5 miles per hour.<\/p>\n<p>Explanation:<br \/>\nThe equation is d = 12.5 \u00d7 t<br \/>\n25 miles \u00f7 2 hours = 12.5 miles\/hour<br \/>\nA direct proportionality d = 12.5 \u00d7 t<\/p>\n<p><strong>3.2 Rate of Change and Slope<\/strong><\/p>\n<p><strong>Find the slope of each line.<\/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-3-Proportional-Relationships-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Model Quiz img 28\" width=\"180\" height=\"186\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\nSlope = 3<\/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-3-Proportional-Relationships-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Model Quiz img 29\" width=\"189\" height=\"185\" \/><br \/>\n______<\/p>\n<p>Answer:<br \/>\nSlope = -5<\/p>\n<p><strong>3.3 Interpreting the Unit Rate as Slope<\/strong><\/p>\n<p>Question 5.<br \/>\nThe distance Train A travels is represented by d = 70t, where d is the distance in kilometers and t is the time in hours. The distance Train B travels at various times is shown in the table. What is the unit rate of each train? Which train is going faster?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Model Quiz img 30\" width=\"235\" height=\"122\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nTrain A: 70 km per hour; Train B: 75 km per hour; Train B is faster.<\/p>\n<p>Explanation:<br \/>\nThe distance Train A travels is represented by d = 70t<br \/>\nwhere d is the distance in kilometers and t is the time in hours<br \/>\nThe speed of train A is 70 kilometer per hour<br \/>\nTo find the speed of train B use the table<br \/>\nSlope = (300 &#8211; 150)\/(4 &#8211; 2) = 75<br \/>\nThe speed of train B is 75 km per hour<br \/>\nThe speed of train B is more<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 6.<br \/>\nWhat is the relationship among proportional relationships, lines, rates of change, and slope?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe relationship between the x-axis and y-axis of any graph is a proportional Relationship which is defined by slope i.e. calculating the rate of change of the plotted line.<br \/>\n1) Here proportional change and rate of change are algebraic quantities which specify how one quantity changes with respect to another.<br \/>\n2) Line and Slope are geometric quantities which describe the graph of any equation.<\/p>\n<h3><a id=\"\u00b7_Mixed_Review_\u2013_Page_No._90\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 90<\/h3>\n<p>Question 1.<br \/>\nWhich of the following is equivalent to 5<sup>-1<\/sup>?<br \/>\nOptions:<br \/>\na. 4<br \/>\nb. \\(\\frac{1}{5}\\)<br \/>\nc. \u2212\\(\\frac{1}{5}\\)<br \/>\nd. -5<\/p>\n<p>Answer:<br \/>\nb. \\(\\frac{1}{5}\\)<\/p>\n<p>Explanation:<br \/>\n5<sup>-1<\/sup><br \/>\n1\/5<\/p>\n<p>Question 2.<br \/>\nPrasert earns $9 an hour. Which table represents this proportional relationship?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-31.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Mixed Review img 31\" width=\"350\" height=\"277\" \/><br \/>\nOptions:<br \/>\na. A<br \/>\nb. B<br \/>\nc. C<br \/>\nd. D<\/p>\n<p>Answer:<br \/>\na. A<\/p>\n<p>Explanation:<br \/>\na. 36\/4 = 9; 54\/6 = 9; 72\/8 = 9<br \/>\nb. 36\/4 = 9; 45\/6 = 7.5; 54\/8 = 6.75<br \/>\nc. 9\/2 = 4.5<br \/>\nd. 18\/2 = 9; 27\/3 = 9; 54\/4 = 13.5<\/p>\n<p>Question 3.<br \/>\nA factory produces widgets at a constant rate. After 4 hours, 3,120 widgets have been produced. At what rate are the widgets being produced?<br \/>\nOptions:<br \/>\na. 630 widgets per hour<br \/>\nb. 708 widgets per hour<br \/>\nc. 780 widgets per hour<br \/>\nd. 1,365 widgets per hour<\/p>\n<p>Answer:<br \/>\nc. 780 widgets per hour<\/p>\n<p>Explanation:<br \/>\nA factory produces widgets at a constant rate. After 4 hours, 3,120 widgets have been produced.<br \/>\n3,120\/4 = 780 widgets per hour<\/p>\n<p>Question 4.<br \/>\nA full lake begins dropping at a constant rate. After 4 weeks it has dropped 3 feet. What is the unit rate of change in the lake\u2019s level compared to its full level?<br \/>\nOptions:<br \/>\na. 0.75 feet per week<br \/>\nb. 1.33 feet per week<br \/>\nc. -0.75 feet per week<br \/>\nd. -1.33 feet per week<\/p>\n<p>Answer:<br \/>\nc. -0.75 feet per week<\/p>\n<p>Explanation:<br \/>\nA full lake begins dropping at a constant rate. After 4 weeks it has dropped 3 feet.<br \/>\n(-3 ft)\/(4 weeks) = -3\/4 ft\/wk = -0.75 ft\/wk<\/p>\n<p>Question 5.<br \/>\nWhat is the slope of the line below?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-32.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Mixed Review img 32\" width=\"252\" height=\"184\" \/><br \/>\nOptions:<br \/>\na. -2<br \/>\nb. \u2212\\(\\frac{1}{2}\\)<br \/>\nc. \\(\\frac{1}{2}\\)<br \/>\nd. 2<\/p>\n<p>Answer:<br \/>\nc. \\(\\frac{1}{2}\\)<\/p>\n<p>Explanation:<br \/>\n(-1.5, 1.5) &amp; (1.5, 0)<br \/>\n(0 &#8211; 1..5)\/(1.5 &#8211; (-1.5))<br \/>\n1.5\/3<br \/>\n= 1\/2<\/p>\n<p>Question 6.<br \/>\nJim earns $41.25 in 5 hours. Susan earns $30.00 in 4 hours. Pierre\u2019s hourly rate is less than Jim\u2019s, but more than Susan\u2019s. What is his hourly rate?<br \/>\nOptions:<br \/>\na. $6.50<br \/>\nb. $7.75<br \/>\nc. $7.35<br \/>\nd. $8.25<\/p>\n<p>Answer:<br \/>\nb. $7.75<\/p>\n<p>Explanation:<br \/>\nJim earns $41.25 in 5 hours.<br \/>\n$41.25\/5 = 8.25<br \/>\nJim&#8217;s unit rate is $8.25 per hour<br \/>\n30\/4 = 7.5<br \/>\nPierre&#8217;s hourly rate is is less than $8.25 but more than $7.50<br \/>\n$7.75<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 7.<br \/>\nJoelle can read 3 pages in 4 minutes, 4.5 pages in 6 minutes, and 6 pages in 8 minutes.<br \/>\na. Make a table of the data.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-3-Proportional-Relationships-img-33.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships Mixed Review img 33\" width=\"337\" height=\"72\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-8-300x53.jpg\" alt=\"Grade 8 Chapter 3 image 8\" width=\"300\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-8-300x53.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-8.jpg 596w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nJoelle can read 3 pages in 4 minutes,<br \/>\ny\/x = 3\/4<br \/>\ny = 3\/4 x<br \/>\nIf x = 6, y = 3\/4 \u00d7 6 = 4.5<br \/>\nIf x = 8, y = 3\/4 \u00d7 8 = 6<\/p>\n<p>Question 7.<br \/>\nb. Use the values in the table to find the unit rate.<br \/>\n_______ pages per minute<\/p>\n<p>Answer:<br \/>\n0.75 pages per minute<\/p>\n<p>Explanation:<br \/>\n3\/4 = 0.75<br \/>\n4.5\/6 = 0.75<br \/>\n6\/8 = 0.75<br \/>\nThe unit rate is 0.75 pages per minute<\/p>\n<p>Question 7.<br \/>\nc. Graph the relationship between minutes and pages read.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-9-300x186.jpg\" alt=\"Grade 8 Chapter 3 image 9\" width=\"300\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-9-300x186.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-3-image-9.jpg 611w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3>Conclusion:<\/h3>\n<p>I wish the info prevailed regarding the Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships PDF is beneficial for you. Share this pdf with your besties in order to help them to overcome the difficulties in maths. Students can definitely score good marks in the exam with the help of the Go Math 8th Grade Ch 3 Proportional Relationships Solution Key.All the Best!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Who doesn\u2019t love the best learning? HMH Grade 8 Go Math Answer Key Chapter 3 Proportional Relationships is the perfect guide for students who love maths. Pupils can habituate practice maths if they start their practice with Go Math 8th Grade Chapter 3 Proportional Relationships Solution Key. The Go Math Grade 8 Answer Key includes &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-3-proportional-relationships\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 3 Proportional Relationships\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":8776,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/go-math-grade-8-chapter-3-proportional-relationships-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6379"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=6379"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6379\/revisions"}],"predecessor-version":[{"id":92804,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6379\/revisions\/92804"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8776"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=6379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=6379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=6379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}