{"id":6475,"date":"2022-03-27T18:26:27","date_gmt":"2022-03-27T12:56:27","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6475"},"modified":"2022-04-07T12:48:24","modified_gmt":"2022-04-07T07:18:24","slug":"go-math-grade-8-answer-key-chapter-5-writing-linear-equations","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-5-writing-linear-equations\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations"},"content":{"rendered":"<p>It is essential for the students to have the best material to study for the exams. Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations recommend to every student who wants to succeed in math. Fall in love with math by practicing the problems from Go Math 8th Grade Chapter 5 Writing Linear Equations Solution Key. We have provided the step by step explanation for each and every question in CCSS Math Answers. Quick &amp; smart learning is possible with the <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> Chapter 5 Writing Linear EquationsPDF.<\/p>\n<h2>Go Math Grade 8 Chapter 5 Writing Linear Equations Answer Key<\/h2>\n<p>The students who are willing to become masters in maths are suggested to follow our Go Math 8th Grade Chapter 5 Writing Linear Equations Solution Key. You can get free access for Go Math Grade 8 Answer Key Chapter 5 Writing Linear equations topicwise here. Check out the topics of Writing Linear equations from the below section.<\/p>\n<p><strong>Lesson 1: Writing Linear Equations from Situations and Graphs\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._130\">\u00b7 Writing Linear Equations from Situations and Graphs \u2013 Page No. 130<\/a><\/li>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._131\">\u00b7 Writing Linear Equations from Situations and Graphs \u2013 Page No. 131<\/a><\/li>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._132\">\u00b7 Writing Linear Equations from Situations and Graphs \u2013 Page No. 132<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Writing Linear Equations from a Table<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._136\">\u00b7 Writing Linear Equations from a Table \u2013 Page No. 136<\/a><\/li>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._137\">\u00b7 Writing Linear Equations from a Table \u2013 Page No. 137<\/a><\/li>\n<li><a href=\"#\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._138\">\u00b7 Writing Linear Equations from a Table \u2013 Page No. 138<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Linear Relationships and Bivariate Data<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._144\">\u00b7 Linear Relationships and Bivariate Data \u2013 Page No. 144<\/a><\/li>\n<li><a href=\"#\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._145\">\u00b7 Linear Relationships and Bivariate Data \u2013 Page No. 145<\/a><\/li>\n<li><a href=\"#\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._146\">\u00b7 Linear Relationships and Bivariate Data \u2013 Page No. 146<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Model_Quiz_\u2013_Page_No._147\">\u00b7 Model Quiz \u2013 Page No. 147<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Mixed_Review_\u2013_Page_No._148\">\u00b7 Mixed Review \u2013 Page No. 148<\/a><\/li>\n<\/ul>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._130\"><\/a>Guided Practice &#8211; Writing Linear Equations from Situations and Graphs &#8211; Page No. 130<\/h3>\n<p>Question 1.<br \/>\nLi is making beaded necklaces. For each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length. Write an equation to find how many beads Li needs for each necklace.<br \/>\na. input variable:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe length of the necklace in inches<\/p>\n<p>Question 1.<br \/>\nb. output variable:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe total number of beads in the necklace<\/p>\n<p>Question 1.<br \/>\nc. equation:<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 5x<\/p>\n<p>Question 2.<br \/>\nKate is planning a trip to the beach. She estimates her average speed to graph her expected progress on the trip. Write an equation in slope-intercept form that represents the situation.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 1\" width=\"184\" height=\"201\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -60x + 300<\/p>\n<p>Explanation:<br \/>\nChoose two points on the graph to find the slope.<br \/>\nFind the slope<br \/>\nm = (y2 -y1)\/(x2 &#8211; x1)<br \/>\nm = -300\/5 = -60<br \/>\nRead the y-intercept from the graph: b = 300<br \/>\nUse your slope and y-intercept values to write an equation in slope-intercept<br \/>\nform.<br \/>\ny = -60x + 300<\/p>\n<p>Question 3.<br \/>\nAt 59 \u00b0F, crickets chirp at a rate of 76 times per minute, and at 65 \u00b0F, they chirp 100 times per minute. Write an equation in slope-intercept form that represents the situation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 4x &#8211; 160<\/p>\n<p>Explanation:<br \/>\nInput variable: Temperature<br \/>\nOutput variable: Number of chirps per minute<br \/>\nSlope:<br \/>\nm = (y2 -y1)\/(x2 &#8211; x1) = (100 &#8211; 76)\/(65 &#8211; 59) = 24\/6 = 4<br \/>\n100 = 4(65) + b<br \/>\ny-intercept:<br \/>\nb = -160<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 4 and b = -160.<br \/>\ny = 4x &#8211; 160<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 4.<br \/>\nExplain what m and b in the equation y = mx + b tell you about the graph of the line with that equation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.<br \/>\nm = change in y-value\/change in x-value<br \/>\nThe y-intercept of this line is the value of y at the point where the line crosses the y-axis.<\/p>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._131\"><\/a>Independent Practice &#8211; Writing Linear Equations from Situations and Graphs &#8211; Page No. 131<\/h3>\n<p>Question 5.<br \/>\nA dragonfly can beat its wings 30 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the dragonfly beats its wings<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 30x<\/p>\n<p>Explanation:<br \/>\nThe linear equation is y = mx + b where m is the slope and b is the y-intercept.<br \/>\ny variable will be the number of times the dragonfly has beat its wings and the x variable will be the time.<br \/>\nA dragonfly can beat its wings 30 times per second.<br \/>\nTo find b, let&#8217;s consider how many times the dragonfly has beat its wings at time 0s.<br \/>\nSo, the equation of the line is y = 30x<\/p>\n<p>Question 6.<br \/>\nA balloon is released from the top of a platform that is 50 meters tall. The balloon rises at the rate of 4 meters per second. Write an equation in slope-intercept form that tells the height of the balloon above the ground after a given number of seconds.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 4x + 50<\/p>\n<p>Explanation:<br \/>\nInput variable: Number of seconds<br \/>\nOutput variable: Height of the balloon<br \/>\nThe balloon rises at a rate of 4 meters per second. m = 4;<br \/>\nA balloon is released from the top of a platform that is 50 meters tall. b = 50.<br \/>\ny = 4x + 50<\/p>\n<p><strong>The graph shows a scuba diver\u2019s ascent over time.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 2\" width=\"278\" height=\"243\" \/><\/p>\n<p>Question 7.<br \/>\nUse the graph to find the slope of the line. Tell what the slope means in this context.<br \/>\nSlope = _______ meters per second<\/p>\n<p>Answer:<br \/>\nSlope = 1\/8 or 0.125 meters per second<\/p>\n<p>Explanation:<br \/>\n10m\/80sec = 1\/8<br \/>\nThe scuba diver\u2019s ascent gives up 1 meter per 16 seconds.<\/p>\n<p>Question 8.<br \/>\nIdentify the y-intercept. Tell what the y-intercept means in this context.<br \/>\ny-intercept = _______ meters<\/p>\n<p>Answer:<br \/>\ny-intercept = -10 meters<\/p>\n<p>Explanation:<br \/>\nThe scuba divers start 10 meters below the water surface<\/p>\n<p>Question 9.<br \/>\nWrite an equation in slope-intercept form that represents the diver\u2019s depth over time.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 1\/8 x &#8211; 10<\/p>\n<p>Question 10.<br \/>\nThe formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0\u00b0C, or 32\u00b0F, and it boils at 100\u00b0C, or 212\u00b0F. Find the slope and y-intercept for a graph that gives degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis. Then write an equation in slope-intercept form that converts degrees Celsius into degrees Fahrenheit.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nInput variable: Celsius<br \/>\nOutput variable: Fahrenheit<br \/>\n(0, 32) (100, 212)<br \/>\nm = (y2 -y1)\/(x2 &#8211; x1) = (212 &#8211; 32)\/(100 &#8211; 0) = 180\/100 = 1.8<br \/>\ny intercepts = 32 when x = 0<br \/>\nF = 1.8C + 32<\/p>\n<p>Question 11.<br \/>\nThe cost of renting a sailboat at a lake is $20 per hour plus $12 for lifejackets. Write an equation in slope-intercept form that can be used to calculate the total amount you would pay for using this sailboat.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 20x + 12<\/p>\n<p>Explanation:<br \/>\nInput variable: Number of hours sailboat is rented<br \/>\nOutput variable: Total cost<br \/>\nThe cost of renting a sailboat at a lake is $20 per hour plus $12 for lifejackets.<br \/>\nSlope m = 20; y-intercept b = 12<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 20 and b = 12.<br \/>\ny = 20x + 12<\/p>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_Situations_and_Graphs_\u2013_Page_No._132\"><\/a>Writing Linear Equations from Situations and Graphs &#8211; Page No. 132<\/h3>\n<p><strong>The graph shows the activity in a savings account.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 1: Writing Linear Equations from Situations and Graphs img 3\" width=\"255\" height=\"172\" \/><\/p>\n<p>Question 12.<br \/>\nWhat was the amount of the initial deposit that started this savings account?<br \/>\n$ _______<\/p>\n<p>Answer:<br \/>\n$1000<\/p>\n<p>Explanation:<br \/>\nThe amount of the initial deposit that started this savings account is $1000<\/p>\n<p>Question 13.<br \/>\nFind the slope and y-intercept of the graphed line.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nslope = 500<br \/>\ny-intercept = 1000<\/p>\n<p>Explanation:<br \/>\nslope m = (y2 -y1)\/(x2 &#8211; x1) = (2000 &#8211; 1500)\/(2 &#8211; 1) = 500\/1 = 500<br \/>\ny-intercept = 1000<\/p>\n<p>Question 14.<br \/>\nWrite an equation in slope-intercept form for the activity in this savings account.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 500x + 1000<\/p>\n<p>Explanation:<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 500 and b = 1000.<br \/>\ny = 500x + 1000<\/p>\n<p>Question 15.<br \/>\nExplain the meaning of the slope in this graph.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe slope represents the amount of money saved in dollars per month in the plan.<\/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 \/>\nExplain how you decide which part of a problem will be represented by the variable x, and which part will be represented by the variable y in a graph of the situation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny=mx+b<br \/>\nM-slope<br \/>\nB-Y intercept<br \/>\nand<br \/>\n(x,y)- would be any point on the graph and if you were to plug those points in for x and y the equation would solve if done properly<\/p>\n<p>Question 17.<br \/>\nRepresent Real-World Problems<br \/>\nDescribe what would be true about the rate of change in a situation that could not be represented by a graphed line and an equation in the form y = mx + b.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe rate of change would not be constant. Using different pairs of points in the slope formula would give different results.<\/p>\n<p>Question 18.<br \/>\nDraw Conclusions<br \/>\nMust m, in the equation y = mx + b, always be a positive number? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo; The slope m can be negative or positive. If the slope of the number is positive (the graph goes upward from left to right), then m will be positive, but if the slope is negative (the graph goes down from left to right), then m is negative.<\/p>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._136\"><\/a>Guided Practice &#8211; Writing Linear Equations from a Table &#8211; Page No. 136<\/h3>\n<p>Question 1.<br \/>\nJaime purchased a $20 bus pass. Each time he rides the bus, a certain amount is deducted from the pass. The table shows the amount, y, left on his pass after x rides. Graph the data, and find the slope and y-intercept from the graph or from the table. Then write the equation for the graph in slope-intercept form.<br \/>\n<img loading=\"lazy\" class=\"\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 4\" width=\"702\" height=\"265\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-1-1-300x172.jpg\" alt=\"Grade 8 Chapter 5 image 1\" width=\"297\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-1-1-300x172.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-1-1.jpg 578w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><br \/>\ny = -5\/4 x + 20<\/p>\n<p>Explanation:<br \/>\nSlope = -20\/16 = -5\/4 = -1.25<br \/>\ny- intercepts = 20<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -1.25 and b = 20.<br \/>\ny = -5\/4 x + 20<\/p>\n<p><strong>The table shows the temperature (y) at different altitudes (x). This is a linear relationship.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 5\" width=\"594\" height=\"80\" \/><\/p>\n<p>Question 2.<br \/>\nFind the slope for this relationship.<br \/>\n_______<\/p>\n<p>Answer:<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (51 &#8211; 59)\/(2000 &#8211; 0) = -8\/2000 = -0.004<\/p>\n<p>Explanation:<br \/>\n(x1, y1) = (0, 59), (x2, y2) = (2000, 51)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (51 &#8211; 59)\/(2000 &#8211; 0) = -8\/2000 = -0.004<\/p>\n<p>Question 3.<br \/>\nFind the y-intercept for this relationship.<br \/>\ny-intercept = _______<\/p>\n<p>Answer:<br \/>\nb = 50<\/p>\n<p>Explanation:<br \/>\ny-intercept = 59 when x = 0<\/p>\n<p>Question 4.<br \/>\nWrite an equation in slope-intercept form that represents this relationship.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -0.004x + 59<\/p>\n<p>Explanation:<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.004 and b = 59.<\/p>\n<p>Question 5.<br \/>\nUse your equation to determine the temperature at an altitude of 5000 feet.<br \/>\n_______ \u00b0F<\/p>\n<p>Answer:<br \/>\n39\u00b0F<\/p>\n<p>Explanation:<br \/>\ny = -0.004x + 59<br \/>\ny = -0.004(5000) + 59 = -20 + 59 = 39<br \/>\nThe temperature is 39\u00b0F at the altitude of 5000 feet.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nDescribe how you can use the information in a table showing a linear relationship to find the slope and y-intercept for the equation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nUse any two points from the table to fins teh slope.<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1)<br \/>\nIf the value of y-intercept, when x=0 is not given in the table, use the slope and any ordered pair from the table and substitute in slope-intercept from y=mx + b to find b.<\/p>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._137\"><\/a>Independent Practice &#8211; Writing Linear Equations from a Table &#8211; Page No. 137<\/h3>\n<p>Question 7.<br \/>\nThe table shows the costs of a large cheese pizza with toppings at a local pizzeria. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 6\" width=\"669\" height=\"215\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-2-300x169.jpg\" alt=\"Grade 8 Chapter 5 image 2\" width=\"300\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-2-300x169.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-2.jpg 584w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Slope m = (y2 -y1)\/(x2 &#8211; x1) = (10 &#8211; 8)\/(1 &#8211; 0) = 2\/1 = 2<br \/>\ny-intercept b = 8<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2 and b = 8.<br \/>\ny = 2x + 8<\/p>\n<p>Question 8.<br \/>\nThe table shows how much an air-conditioning repair company charges for different numbers of hours of work. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 7\" width=\"730\" height=\"204\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-3-300x174.jpg\" alt=\"Grade 8 Chapter 5 image 3\" width=\"300\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-3-300x174.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-3.jpg 574w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Slope m = (y2 -y1)\/(x2 &#8211; x1) = (100 &#8211; 50)\/(1 &#8211; 0) = 50\/1 = 50<br \/>\ny-intercept\u00a0b = 50<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 50 and b = 50.<br \/>\ny = 50x + 50<\/p>\n<p>Question 9.<br \/>\nA friend gave Ms. Morris a gift card for a local car wash. The table shows the linear relationship of how the value left on the card relates to the number of car washes.<br \/>\na. Write an equation that shows the number of dollars left on the card.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 8\" width=\"377\" height=\"73\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -1.50x + 30<\/p>\n<p>Explanation:<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (18 &#8211; 30)\/(8 &#8211; 0) = -12\/8 = -1.5<br \/>\ny-intercept b = 30<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -1.50 and b = 30.<br \/>\ny = -1.50x + 30<\/p>\n<p>Question 9.<br \/>\nb. Explain the meaning of the negative slope in this situation.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe negative slope means that the amount on the card decreased by $1.5 per car wash<\/p>\n<p>Question 9.<br \/>\nc. What is the maximum value of x that makes sense in this context? Explain.<br \/>\nx = _______<\/p>\n<p>Answer:<br \/>\nx = 20<\/p>\n<p>Explanation:<br \/>\n0 = -1.50x + 30<br \/>\n1.5x = 30<br \/>\nx = 30\/1.5 = 20<br \/>\nthe maximum value of x = 20<\/p>\n<p><strong>The tables show linear relationships between x and y. Write an equation in slope-intercept form for each relationship.<\/strong><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 9\" width=\"272\" height=\"75\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (3 &#8211; 1)\/(2 &#8211; 0) =\u00a0 2\/2 = 1<br \/>\ny-intercept b = 1<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1 and b = 1.<br \/>\ny =\u00a0 x + 1<\/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-5-Writing-Linear-Equations-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 10\" width=\"273\" height=\"83\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (6 &#8211; 4)\/(0 &#8211; 1) =\u00a0 -2\/1 = -2<br \/>\ny-intercept b = 6<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -2 and b = 6.<br \/>\ny = -2x + 6<\/p>\n<h3><a id=\"\u00b7_Writing_Linear_Equations_from_a_Table_\u2013_Page_No._138\"><\/a>Writing Linear Equations from a Table &#8211; Page No. 138<\/h3>\n<p>Question 12.<br \/>\nFinance<br \/>\nDesiree starts a savings account with $125.00. Every month, she deposits $53.50.<br \/>\na. Complete the table to model the situation.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 11\" width=\"534\" height=\"104\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-7733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-4-300x36.png\" alt=\"Grade 8 Chapter 5 image 4\" width=\"333\" height=\"40\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-4-300x36.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-4.png 590w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 12.<br \/>\nb. Write an equation in slope-intercept form that shows how much money Desiree has in her savings account after x months.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 53.5x + 125<\/p>\n<p>Explanation:<br \/>\nDesiree starts a savings account with $125.00. Every month, she deposits $53.50.<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 53.5 and b = 125.<br \/>\ny = 53.5x + 125<\/p>\n<p>Question 12.<br \/>\nc. Use the equation to find how much money Desiree will have in savings after 11 months.<br \/>\n$ ________<\/p>\n<p>Answer:<br \/>\n$713.5<\/p>\n<p>Explanation:<br \/>\ny = 53.5x + 125<br \/>\nThe value of x is 11<br \/>\ny = 53.5 (11) + 125 = 588.5 + 125 = 713.5<br \/>\nDesiree will have $713.5 in savings after 11 months.<\/p>\n<p>Question 13.<br \/>\nMonty documented the amount of rain his farm received on a monthly basis, as shown in the table.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 2: Writing Linear Equations from a Table img 12\" width=\"409\" height=\"71\" \/><br \/>\na. Is the relationship linear? Why or why not?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nThe change in the months is constant but the change in rainfall is not constant.<\/p>\n<p>Question 13.<br \/>\nb. Can an equation be written to describe the amount of rain? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nThere is no apparent pattern in the given data.<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 14.<br \/>\nAnalyze Relationships<br \/>\nIf you have a table that shows a linear relationship, when can you read the value for b, in y = mx + b, directly from the table without drawing a graph or doing any calculations? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nYou can read the value of b directly from the table whrn the table contains the input value of 0 and its corresponding output values (value of y when x = 0)<\/p>\n<p>Question 15.<br \/>\nWhat If?<br \/>\nJa\u00edme graphed linear data given in the form (cost, number). The y-intercept was 0. Jayla graphed the same data given in the form (number, cost). What was the y-intercept of her graph? Explain.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nJa\u00edme graphed linear data given in the form (cost, number). The y-intercept was 0. Jayla graphed the same data given in the form (number, cost).<br \/>\nJa\u00edme&#8217;s graph contained (0, 0). Since Jayal&#8217;s data were the same y-intercept is 0 but x and y are switched.<\/p>\n<h3><a id=\"\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._144\"><\/a>Guided Practice &#8211; Linear Relationships and Bivariate Data &#8211; Page No. 144<\/h3>\n<p><strong>Use the following graphs to find the equation of the linear relationship.<\/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-5-Writing-Linear-Equations-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 13\" width=\"205\" height=\"203\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 30x<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-5-300x179.png\" alt=\"Grade 8 Chapter 5 image 5\" width=\"300\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-5-300x179.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-5.png 710w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (1, 30) and (x2, y2) = (2, 60)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (60 &#8211; 30)\/(2 &#8211; 1) = 30\/1 = 30<br \/>\ny-intercept b = 0<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 30 and b = 0.<br \/>\ny = 30x<\/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-5-Writing-Linear-Equations-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 14\" width=\"191\" height=\"214\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 2.5x + 2<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-6-300x178.png\" alt=\"Grade 8 Chapter 5 image 6\" width=\"300\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-6-300x178.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-6.png 716w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (2, 7) and (x2, y2) = (4, 12)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (12 &#8211; 7)\/(4 &#8211; 2) = 5\/2 = 2.5<br \/>\ny-intercept b = 2<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2.5 and b = 2.<br \/>\ny = 2.5x + 2<\/p>\n<p>Question 3.<br \/>\nThe graph shows the relationship between the number of hours a kayak is rented and the total cost of the rental. Write an equation of the relationship. Then use the equation to predict the cost of a rental that lasts 5.5 hours.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 15\" width=\"408\" height=\"257\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 20x + 30<br \/>\nThe cost of a rental that lasts 5.5 hours is $140<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (2, 70) and (x2, y2) = (4, 110)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (110 &#8211; 70)\/(4 &#8211; 2) = 40\/2 = 20<br \/>\ny-intercept b = 30<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 20 and b = 30.<br \/>\ny = 20x + 30<br \/>\nSubstitue the value of x is 5.5 hrs<br \/>\ny = 20 (5.5) + 30<br \/>\ny = 110 + 30 = 140<br \/>\nThe cost of a rental that lasts 5.5 hours is $140<\/p>\n<p><strong>Does each of the following graphs represent a linear relationship? Why or why not?<\/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-5-Writing-Linear-Equations-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 16\" width=\"206\" height=\"201\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nYes; The graph has a constant rate of change<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (2, 6) and (x2, y2) = (5, 15)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (15 &#8211; 6)\/(5 &#8211; 2) = 9\/3 = 3<br \/>\ny-intercept b = 6<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 3 and b = 6.<br \/>\ny = 3x + 6<br \/>\nThe values changing according to the constant change in the x values.<\/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-5-Writing-Linear-Equations-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 17\" width=\"174\" height=\"272\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo; The graph does not have a constant rate of change<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 6.<br \/>\nHow can you tell if a set of bivariate data shows a linear relationship?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nIt is a linear relationship if the rate of change is constant or the graph is a straight line.<\/p>\n<h3><a id=\"\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._145\"><\/a>Independent Practice &#8211; Linear Relationships and Bivariate Data &#8211; Page No. 145<\/h3>\n<p><strong>Does each of the following tables represent a linear relationship? Why or why not?<\/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-5-Writing-Linear-Equations-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 18\" width=\"218\" height=\"145\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nLinear Relationship<\/p>\n<p>Explanation:<br \/>\nFind Rate of Change using Slope m = (y2 -y1)\/(x2 &#8211; x1)<br \/>\nRate of Change = (45 &#8211; 15)\/(9 &#8211; 3) = 30\/6 = 5<br \/>\nRate of Change = (105 &#8211; 45)\/(21 &#8211; 9) = 60\/12 = 5<br \/>\nIt is a Linear Relationship as the rate of the change is constant.<\/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-5-Writing-Linear-Equations-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 19\" width=\"208\" height=\"126\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nnot a Linear Relationship<\/p>\n<p>Explanation:<br \/>\nFind Rate of Change using Slope m = (y2 -y1)\/(x2 &#8211; x1)<br \/>\nRate of Change = (76.8 &#8211; 30)\/(8 &#8211; 5) = 46.\/3 = 15.6<br \/>\nRate of Change = (235.2 &#8211; 76.8)\/(14 &#8211; 8) = 158.4\/6 = 26.4<br \/>\nIt is not a Linear Relationship as the rate of the change is varies.<\/p>\n<p><strong>Explain whether or not you think each relationship is linear.<\/strong><\/p>\n<p>Question 9.<br \/>\nthe cost of equal-priced DVDs and the number purchased<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = cx<\/p>\n<p>Explanation:<br \/>\nThe relation between the cost of equal-priced DVDs and the number purchased is linear because the change rate is constant. If we denote with c the cost of a DVD, with x the number of purchased DVDs and with y the total cost of the purchased DVDs, we get an equation of the form:<br \/>\ny = cx<\/p>\n<p>Question 10.<br \/>\nthe height of a person and the person\u2019s age<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNon &#8211; Linear relationship<\/p>\n<p>Explanation:<br \/>\nThe height of a person does not increase at a constant rate with a person&#8217;s age<\/p>\n<p>Question 11.<br \/>\nthe area of a square quilt and its side length<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNon &#8211; Linear relationship<\/p>\n<p>Explanation:<br \/>\nThe rate of change in the area of a square quilt increase as the side length increases.<\/p>\n<p>Question 12.<br \/>\nthe number of miles to the next service station and the number of kilometers<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nLinear relationship<\/p>\n<p>Explanation:<br \/>\nThe number of miles increases at a constant rate with the number of kilometers.<\/p>\n<p>Question 13.<br \/>\nMultistep<br \/>\nThe Mars Rover travels 0.75 feet in 6 seconds. Add the point to the graph. Then determine whether the relationship between distance and time is linear, and if so, predict the distance that the Mars Rover would travel in 1 minute.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 20\" width=\"312\" height=\"363\" \/><br \/>\nDistance traveled in 1 min.: _______ ft.<\/p>\n<p>Answer:<br \/>\nRelationship is linear<br \/>\nDistance traveled in 1 min.: 7.5 ft.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-7-300x178.png\" alt=\"Grade 8 Chapter 5 image 7\" width=\"300\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-7-300x178.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-7.png 718w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe graph is a straight line. So, the Relationship is linear<br \/>\nThe equation representing the relationship between distance and time.<br \/>\ny = 0.125x<br \/>\nThe value of x is 1 min = 60 sec<br \/>\ny = 0.125 (60) = 7.5 ft<br \/>\nDistance traveled in 1 min.: 7.5 ft.<\/p>\n<h3><a id=\"\u00b7_Linear_Relationships_and_Bivariate_Data_\u2013_Page_No._146\"><\/a>Linear Relationships and Bivariate Data &#8211; Page No. 146<\/h3>\n<p>Question 14.<br \/>\nMake a Conjecture<br \/>\nZefram analyzed a linear relationship, found that the slope-intercept equation was y=3.5x+16, and made a prediction for the value of y for a given value of x. He realized that he made an error calculating the y-intercept and that it was actually 12. Can he just subtract 4 from his prediction if he knows that the slope is correct? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nThe value of y is calculated using y = 3.5x+ 16. Since the slope of the point remains the same, 4 can be subtracted from the predicted answer as the value of y would be: y = 3.5x+ 16 &#8211; 4<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 15.<br \/>\nCommunicate Mathematical Ideas<br \/>\nThe table shows a linear relationship. How can you predict the value of y when x = 6 without finding the equation of the relationship?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Lesson 3: Linear Relationships and Bivariate Data img 21\" width=\"215\" height=\"130\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n57<\/p>\n<p>Explanation:<br \/>\nFind Rate of Change using Slope m = (y2 -y1)\/(x2 &#8211; x1)<br \/>\nRate of Change = (76 &#8211; 38)\/(8 &#8211; 4) = 38\/4 = 9.5<br \/>\nSince the difference between 8 and S is 2, subtract twice the value of the rate of change from 76<br \/>\ny = 76 &#8211; (9.5 \u00d7 2) =57<\/p>\n<p>Question 16.<br \/>\nCritique Reasoning<br \/>\nLouis says that if the differences between the values of x are constant between all the points on a graph, then the relationship is linear. Do you agree? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nThe difference between y should be constant for a constant interval of x.<\/p>\n<p>Question 17.<br \/>\nMake a Conjecture<br \/>\nSuppose you know the slope of a linear relationship and one of the points that its graph passes through. How could you predict another point that falls on the graph of the line?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFind the equation of the linear relationship using the slope and given point. The insert any x-value to find a y value on the graph of the line.<\/p>\n<p>Question 18.<br \/>\nExplain the Error<br \/>\nThomas used (7, 17.5) and (18, 45) from a graph to find the equation of a linear relationship as shown. What was his mistake?<br \/>\nm = \\(\\frac{45-7}{18-17.5}=\\frac{38}{0.5}\\) = 79<br \/>\ny = 79x + b =<br \/>\n49 = 79 \u00d7 18 + b<br \/>\n45 = 1422 + b, so b = \u22121337<br \/>\nThe equation is y = 79x \u2212 1377<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nHe subtracted the x value of the first point from the y of the second point and the y value of the second point from the x value of the first point.<br \/>\nHence, the slope is incorrect and the equation is incorrect as well. The correct slope is<br \/>\n(45 &#8211; 17.5)\/(18 &#8211; 7) = 27.5\/11 = 2.5<\/p>\n<h3><a id=\"\u00b7_Model_Quiz_\u2013_Page_No._147\"><\/a>5.1 Writing Linear Equations from Situations and Graphs &#8211; Model Quiz &#8211; Page No. 147<\/h3>\n<p><strong>Write the equation of each line in slope-intercept form.<\/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-5-Writing-Linear-Equations-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 22\" width=\"153\" height=\"135\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 30x + 20<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (0, 20), (x2, y2) = (2, 80)<br \/>\nSubstitute the value of m and (x1, y1) = (0, 20), (x2, y2) = (2, 80)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (80 &#8211; 20)\/(2 &#8211; 0) = 60\/2 = 30<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n80 = 30(2) + b<br \/>\ny-intercept b = 20<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 30 and b = 20.<br \/>\ny = 30x + 20<\/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-5-Writing-Linear-Equations-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 23\" width=\"154\" height=\"146\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -10x + 60<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (6, 0), (x2, y2) = (0, 60)<br \/>\nSubstitute the value of m and (x1, y1) = (6, 0), (x2, y2) = (0, 60)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (60 &#8211; 0)\/(0 &#8211; 6) = -60\/6 = -10<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n60 = -10(0) + b<br \/>\ny-intercept b = 60<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -10 and b = 60.<br \/>\ny = -10x + 60<\/p>\n<p><strong>5.2 Writing Linear Equations from a Table<\/strong><\/p>\n<p><strong>Write the equation of each linear relationship in slope-intercept form.<\/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-5-Writing-Linear-Equations-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 24\" width=\"238\" height=\"73\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 0.35x + 1.5<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (0, 1.5), (x2, y2) = (100, 36.5)<br \/>\nSubstitute the value of m and (x1, y1) = (0, 1.5), (x2, y2) = (100, 36.5)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (36.5 &#8211; 1.5)\/(100 &#8211; 0) = 35\/100 = 0.35<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n1.5 =0.35(0) + b<br \/>\ny-intercept b = 1.5<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 0.35 and b = 1.5.<br \/>\ny = 0.35x + 1.5<\/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-5-Writing-Linear-Equations-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 25\" width=\"234\" height=\"69\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -0.6x + 109<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (25, 94), (x2, y2) = (35, 88)<br \/>\nSubstitute the value of m and (x1, y1) = (25, 94), (x2, y2) = (35, 88)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (88 &#8211; 94)\/(35 &#8211; 25) = -6\/10 = -0.6<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n88 = -0.6(35) + b<br \/>\ny-intercept b = 109<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.6 and b = 109.<br \/>\ny = -0.6x + 109<\/p>\n<p><strong>5.3 Linear Relationships and Bivariate Data<\/strong><\/p>\n<p><strong>Write the equation of the line that connects each set of data points.<\/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-5-Writing-Linear-Equations-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 26\" width=\"153\" height=\"146\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 2\/3x + 26 2\/3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-8-300x180.png\" alt=\"Grade 8 Chapter 5 image 8\" width=\"300\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-8-300x180.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-8.png 715w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (20, 40), (x2, y2) = (50, 60)<br \/>\nSubstitute the value of m and (x1, y1) = (20, 40), (x2, y2) = (50, 60)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (60 &#8211; 40)\/(50 &#8211; 20) = 20\/30 = 2\/3<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n40 = 2\/3(20) + b<br \/>\ny-intercept b = 26 2\/3<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 2\/3 and b = 26 2\/3.<br \/>\ny = 2\/3x + 26 2\/3<\/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-5-Writing-Linear-Equations-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Model Quiz img 27\" width=\"145\" height=\"140\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = -3x + 140<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-9-300x180.png\" alt=\"Grade 8 Chapter 5 image 9\" width=\"300\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-9-300x180.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-5-image-9.png 714w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (25, 65), (x2, y2) = (30, 50)<br \/>\nSubstitute the value of m and (x1, y1) = (25, 65), (x2, y2) = (30, 50)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (50 &#8211; 65)\/(30 &#8211; 25) = -15\/5 = -3<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n50 = -3(30) + b<br \/>\ny-intercept b = 140<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -3 and b = 140.<br \/>\ny = -3x + 140<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 7.<br \/>\nWrite a real-world situation that can be represented by a linear relationship.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThere is an hourly fee of $15 for renting the ski gears per hour and an entry fee of $10 for the ski lodge.<\/p>\n<h3><a id=\"\u00b7_Mixed_Review_\u2013_Page_No._148\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 148<\/h3>\n<p>Question 1.<br \/>\nAn hourglass is turned over with the top part filled with sand. After 3 minutes, there are 855 mL of sand in the top half. After 10 minutes, there are 750 mL of sand in the top half. Which equation represents this situation?<br \/>\nOptions:<br \/>\na. y = 285x<br \/>\nb. y = \u221210.5x + 900<br \/>\nc. y = \u221215x + 900<br \/>\nd. y = 75x<\/p>\n<p>Answer:<br \/>\nc. y = \u221215x + 900<\/p>\n<p>Explanation:<br \/>\nIdentify the input and output variable<br \/>\nInput: Number of minutes<br \/>\nOutput: Quantity of sand in the hourglass<br \/>\nWrite the given information as ordered pair (3, 855), (10, 750)<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (10, 750), (x2, y2) =(3, 855)<br \/>\nSubstitute the value of m and (x1, y1) = (10, 750), (x2, y2) =(3, 855)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (855 &#8211; 750)\/(3 &#8211; 10) = -105\/7 = -15<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n750 = -15(10) + b<br \/>\ny-intercept b = 900<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -15 and b = 900.<br \/>\ny = -15x + 900<\/p>\n<p>Question 2.<br \/>\nWhich 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-5-Writing-Linear-Equations-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 28\" width=\"192\" height=\"624\" \/><br \/>\nOptions:<br \/>\na. A<br \/>\nb. B<br \/>\nc. C<br \/>\nd. D<\/p>\n<p>Answer:<br \/>\nb. B<\/p>\n<p>Explanation:<br \/>\nGraph B represents the linear relationship<br \/>\nThe data appears to lie on a straight line<\/p>\n<p>Question 3.<br \/>\nWhat are the slope and y-intercept of the relationship shown in the table?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 29\" width=\"284\" height=\"80\" \/><br \/>\nOptions:<br \/>\na. slope = 0.05, y-intercept = 1,500<br \/>\nb. slope = 0.5, y-intercept = 1,500<br \/>\nc. slope = 0.05, y-intercept = 2,000<br \/>\nd. slope = 0.5, y-intercept = 2,000<\/p>\n<p>Answer:<br \/>\nc. slope = 0.05, y-intercept = 2,000<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 &#8211; x1) where (x1, y1) = (10,000, 2,500), (x2, y2) =(20,000, 3,000)<br \/>\nSubstitute the value of m and (x1, y1) = (10,000, 2,500), (x2, y2) =(20,000, 3,000)<br \/>\nSlope m = (y2 -y1)\/(x2 &#8211; x1) = (3,000 &#8211; 2,500)\/(20,000 &#8211; 10,000) = 500\/10,000 = 0.05<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\n3,000 = 0.05(20,000) + b<br \/>\ny-intercept b = 2,000<\/p>\n<p>Question 4.<br \/>\nWhich is the sum of 3.15 \u00d7 10<sup>7<\/sup> + 9.3 \u00d7 10<sup>6<\/sup>? Write your answer in scientific notation.<br \/>\nOptions:<br \/>\na. 4.08 \u00d7 10<sup>7<\/sup><br \/>\nb. 4.08 \u00d7 10<sup>6<\/sup><br \/>\nc. 0.408 \u00d7 10<sup>8<\/sup><br \/>\nd. 40.8 \u00d7 10<sup>6<\/sup><\/p>\n<p>Answer:<br \/>\na. 4.08 \u00d7 10<sup>7<\/sup><\/p>\n<p>Explanation:<br \/>\nGiven 3.15 \u00d7 10<sup>7<\/sup> + 9.3 \u00d7 10<sup>6<\/sup>?<br \/>\n(3.15 + 0.93) \u00d7 10<sup>7<\/sup><br \/>\n4.08 \u00d7 10<sup>7<\/sup><\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 5.<br \/>\nFranklin\u2019s faucet was leaking, so he put a bucket underneath to catch the water. After a while, Franklin started keeping track of how much water was in the bucket. His data is in the table below.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-5-Writing-Linear-Equations-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations Mixed Review img 30\" width=\"267\" height=\"68\" \/><br \/>\na. Is the relationship linear or nonlinear?<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nThe relationship linear<\/p>\n<p>Explanation:<br \/>\nFind the rate of change by Difference in Quarts\/Hours<br \/>\n(6.5 &#8211; 5)\/(3 &#8211; 2) = 1.5<br \/>\n(8 &#8211; 6.5)\/(4 &#8211; 3) = 1.5<br \/>\n(9.5 &#8211; 8)\/(5 &#8211; 4) = 1.5<br \/>\nSince the rate of change is constant, the relationship is linear.<\/p>\n<p>Question 5.<br \/>\nb. Write the equation for the relationship.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nRate of change is the slope of the linear equation<br \/>\nm = 1.5<\/p>\n<p>Question 5.<br \/>\nc. Predict how much water will be in the bucket after 14 hours if Franklin doesn\u2019t stop the leak.<br \/>\n_______ quarts<\/p>\n<p>Answer:<br \/>\n23 quarts<\/p>\n<p>Explanation:<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y-intercept (b)<br \/>\ny = mx + b<br \/>\n5 = 1.5(2) + b<br \/>\ny-intercept b = 2<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1.5 and b = 2.<br \/>\ny = 1.5x + 2<br \/>\nThe x value is 2<br \/>\ny = 1.5(2) + 2 = 23<br \/>\nThere will be 23 quarts after 14 hrs.<\/p>\n<h3>Conclusion:<\/h3>\n<p>Every expert&#8217;s choice is utilizing Go math Grade 8 Chapter 5 Writing Linear Equations Answer Key PDF. Practice the question from our Go Math 8th Grade Chapter 5 Writing Linear Equations Answers to score the highest marks in the exams. Compare the questions with the real-time problems and solve the problems with the help of Go Math Grade 8 Chapter 5 Answer Key Chapter 5 Writing Linear Equations. Stay tuned to our ccssmathanswers.com to get the all Go Math Grade 8 Answer Key Chapterwise pdfs.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is essential for the students to have the best material to study for the exams. Go Math Grade 8 Answer Key Chapter 5 Writing Linear Equations recommend to every student who wants to succeed in math. 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