{"id":5571,"date":"2021-02-05T19:55:22","date_gmt":"2021-02-05T19:55:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=5571"},"modified":"2025-11-30T03:15:23","modified_gmt":"2025-11-30T03:15:23","slug":"3-2-linear-growth","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/3-2-linear-growth\/","title":{"raw":"3.2 Linear Growth","rendered":"3.2 Linear Growth"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Apply and construct linear models using the form y = mx + b<\/li>\r\n<\/ul>\r\n<\/div>\r\nGraphs and equations that model the real world are called <strong>mathematical models<\/strong>.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05200019\/gas.jpg\"><img class=\"wp-image-5574 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05200019\/gas-300x183.jpg\" alt=\"\" width=\"397\" height=\"242\" \/><\/a>\r\n<h3>Linear Models<\/h3>\r\nSuppose the price of gasoline $2.25 per gallon. To create a graphical model of putting gasoline in a car, we can start with a table. Let's let x represent the number of gallons, and let y represent the price the customer will pay.\r\n<table style=\"width: 246px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 225.217px;\"><strong>x = number of gallons<\/strong><\/td>\r\n<td style=\"width: 121.05px;\"><strong>y = price<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">0<\/td>\r\n<td style=\"width: 121.05px;\">0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">1<\/td>\r\n<td style=\"width: 121.05px;\">$2.25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">2<\/td>\r\n<td style=\"width: 121.05px;\">$4.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">3<\/td>\r\n<td style=\"width: 121.05px;\">$6.75<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">4<\/td>\r\n<td style=\"width: 121.05px;\">$9.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">5<\/td>\r\n<td style=\"width: 121.05px;\">$11.25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">10<\/td>\r\n<td style=\"width: 121.05px;\">$22.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 225.217px;\">20<\/td>\r\n<td style=\"width: 121.05px;\">$45.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05203829\/L1-full1.jpg\"><img class=\"wp-image-5580 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05203829\/L1-full1.jpg\" alt=\"\" width=\"675\" height=\"470\" \/><\/a>\r\n\r\nIn order to create an equation that models the same scenario, we can observe the pattern from the table or the graph.\r\n\r\nIf we put 0 gallons of gas in the car, the price the customer pays is $0. If we put 1 gallon of gas in the car, the price is $2.25. If we put 2 gallons of gas in the car, the price is $4.50. We notice the pattern can be written as:\u00a0 <strong>price = $2.25 times the number of gallons<\/strong>.\r\n\r\nUsing x and y, dropping the dollar sign, and using algebra notation, the pattern can be written as an equation:\u00a0\u00a0 <strong>y = 2.25x<\/strong>\r\n\r\nThis equation can model putting gasoline in a car for any price of gasoline:\r\n<p style=\"text-align: center;\"><strong>price = price per gallon x number of gallons<\/strong><\/p>\r\nNow, suppose in addition to the gasoline, a person also bought a bag of chips at the gas station.<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05204446\/chips.jpg\"><img class=\"size-medium wp-image-5583 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05204446\/chips-300x185.jpg\" alt=\"\" width=\"300\" height=\"185\" \/><\/a>Suppose the price of gasoline is $1.90 per gallon and the chips are $1.25.\r\n<table style=\"width: 248px;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 208.517px;\"><strong>x = number of gallons<\/strong><\/td>\r\n<td style=\"width: 137.75px;\"><strong>y = price<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">0<\/td>\r\n<td style=\"width: 137.75px;\">$1.25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">1<\/td>\r\n<td style=\"width: 137.75px;\">$3.15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">2<\/td>\r\n<td style=\"width: 137.75px;\">$5.05<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">3<\/td>\r\n<td style=\"width: 137.75px;\">$6.95<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">4<\/td>\r\n<td style=\"width: 137.75px;\">$8.85<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">5<\/td>\r\n<td style=\"width: 137.75px;\">$10.75<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">10<\/td>\r\n<td style=\"width: 137.75px;\">$20.25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 208.517px;\">20<\/td>\r\n<td style=\"width: 137.75px;\">$39.25<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05205158\/L2-full.jpg\"><img class=\"wp-image-5584 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05205158\/L2-full.jpg\" alt=\"\" width=\"692\" height=\"390\" \/><\/a>\r\n\r\nIn the scenario of buying chips in addition to gasoline, we have a different pattern. If we put 0 gallons of gas in the car, the price the customer pays is $1.25 (for the chips only). If we put 1 gallon of gas in the car, the price is $3.15 (1 gallon of gas plus the bag of chips). If we put 2 gallons of gas in the car, the price is $5.05 (2 gallons of gas plus the bag of chips).\r\n\r\nWe notice the pattern can be written as:\u00a0 <strong>price = $1.90 times the number of gallons<\/strong> <strong>plus $1.25<\/strong>\r\n\r\nUsing x and y, dropping the dollar sign, and using algebra notation, the pattern can be written as an equation:\u00a0\u00a0 <strong>y = 1.90x + 1.25\r\n<\/strong>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nSuppose gasoline is $2.10 per gallon. A customer also purchases a soda pop for $1.25. Write the equation that models this scenario, where x = the number of gallons of gasoline and y = the price the customer will pay.\r\n\r\n[reveal-answer q=\"996665\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"996665\"]y = 2.10x + 1.25[\/hidden-answer]\r\n\r\n<\/div>\r\nLet's return to the model: <strong>y = 1.90x + 1.25<\/strong>\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05213127\/y-is-mx-plus-b.jpg\"><img class=\"size-medium wp-image-5588 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05213127\/y-is-mx-plus-b-300x208.jpg\" alt=\"\" width=\"300\" height=\"208\" \/><\/a>\r\n\r\nThere are three <strong>terms<\/strong> in the model:\r\n<ul>\r\n \t<li>y is the price the customer will pay<\/li>\r\n \t<li>1.90x tells us that for every gallon of gasoline put in the car, the customer will pay $1.90.<\/li>\r\n \t<li>1.25 is the constant part and does not vary.<\/li>\r\n<\/ul>\r\nIn some models, the constant term is called the <strong>initial amount <\/strong>or <strong>starting amount.<\/strong>\r\n\r\nConsider the scenario of a student saving money to pay for tuition. Suppose the student was given $100 as birthday money. Then, the student saved $25 per week. Let y = total amount saved, and x = the number weeks since beginning to save, the model would be: <strong>y = 25x + 100.<\/strong>\r\n\r\nThe general model for saving money would be:\r\n<p style=\"text-align: center;\"><strong>y = amount saved per week times the number of weeks plus the initial amount.<\/strong><\/p>\r\n\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nSuppose your friend was saving money to buy a car. She started with $400 and is now saving $75 per week from her part-time job. Let y = total amount saved, and x = the number of weeks since beginning to save. Write the equation that models this scenario.\r\n\r\n[reveal-answer q=\"837084\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"837084\"]y = 75x + 400[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\nTo model scenarios involving linear growth, use y = mx + b.\r\n<ul>\r\n \t<li>In algebra, <strong>m<\/strong> is called the <strong>slope<\/strong>.\r\n<ul>\r\n \t<li>In our models, m was the price per gallon, or amount saved per week.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>In algebra, <strong>b<\/strong> is called the <strong>y-intercept<\/strong>.\r\n<ul>\r\n \t<li>In our models, b was the price of the snack purchased at the gas station, or the starting amount in a savings plan.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The term <strong>mx<\/strong> models the part of the scenario that changes (the variable part).<\/li>\r\n \t<li>The term <strong>b<\/strong> models the <strong>constant<\/strong> or <strong>fixed<\/strong> part of the scenario, which does not change.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Apply and construct linear models using the form y = mx + b<\/li>\n<\/ul>\n<\/div>\n<p>Graphs and equations that model the real world are called <strong>mathematical models<\/strong>.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05200019\/gas.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5574 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05200019\/gas-300x183.jpg\" alt=\"\" width=\"397\" height=\"242\" \/><\/a><\/p>\n<h3>Linear Models<\/h3>\n<p>Suppose the price of gasoline $2.25 per gallon. To create a graphical model of putting gasoline in a car, we can start with a table. Let&#8217;s let x represent the number of gallons, and let y represent the price the customer will pay.<\/p>\n<table style=\"width: 246px;\">\n<tbody>\n<tr>\n<td style=\"width: 225.217px;\"><strong>x = number of gallons<\/strong><\/td>\n<td style=\"width: 121.05px;\"><strong>y = price<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">0<\/td>\n<td style=\"width: 121.05px;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">1<\/td>\n<td style=\"width: 121.05px;\">$2.25<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">2<\/td>\n<td style=\"width: 121.05px;\">$4.50<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">3<\/td>\n<td style=\"width: 121.05px;\">$6.75<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">4<\/td>\n<td style=\"width: 121.05px;\">$9.00<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">5<\/td>\n<td style=\"width: 121.05px;\">$11.25<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">10<\/td>\n<td style=\"width: 121.05px;\">$22.50<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 225.217px;\">20<\/td>\n<td style=\"width: 121.05px;\">$45.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05203829\/L1-full1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5580 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05203829\/L1-full1.jpg\" alt=\"\" width=\"675\" height=\"470\" \/><\/a><\/p>\n<p>In order to create an equation that models the same scenario, we can observe the pattern from the table or the graph.<\/p>\n<p>If we put 0 gallons of gas in the car, the price the customer pays is $0. If we put 1 gallon of gas in the car, the price is $2.25. If we put 2 gallons of gas in the car, the price is $4.50. We notice the pattern can be written as:\u00a0 <strong>price = $2.25 times the number of gallons<\/strong>.<\/p>\n<p>Using x and y, dropping the dollar sign, and using algebra notation, the pattern can be written as an equation:\u00a0\u00a0 <strong>y = 2.25x<\/strong><\/p>\n<p>This equation can model putting gasoline in a car for any price of gasoline:<\/p>\n<p style=\"text-align: center;\"><strong>price = price per gallon x number of gallons<\/strong><\/p>\n<p>Now, suppose in addition to the gasoline, a person also bought a bag of chips at the gas station.<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05204446\/chips.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5583 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05204446\/chips-300x185.jpg\" alt=\"\" width=\"300\" height=\"185\" \/><\/a>Suppose the price of gasoline is $1.90 per gallon and the chips are $1.25.<\/p>\n<table style=\"width: 248px;\">\n<tbody>\n<tr>\n<td style=\"width: 208.517px;\"><strong>x = number of gallons<\/strong><\/td>\n<td style=\"width: 137.75px;\"><strong>y = price<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">0<\/td>\n<td style=\"width: 137.75px;\">$1.25<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">1<\/td>\n<td style=\"width: 137.75px;\">$3.15<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">2<\/td>\n<td style=\"width: 137.75px;\">$5.05<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">3<\/td>\n<td style=\"width: 137.75px;\">$6.95<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">4<\/td>\n<td style=\"width: 137.75px;\">$8.85<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">5<\/td>\n<td style=\"width: 137.75px;\">$10.75<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">10<\/td>\n<td style=\"width: 137.75px;\">$20.25<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 208.517px;\">20<\/td>\n<td style=\"width: 137.75px;\">$39.25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05205158\/L2-full.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5584 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05205158\/L2-full.jpg\" alt=\"\" width=\"692\" height=\"390\" \/><\/a><\/p>\n<p>In the scenario of buying chips in addition to gasoline, we have a different pattern. If we put 0 gallons of gas in the car, the price the customer pays is $1.25 (for the chips only). If we put 1 gallon of gas in the car, the price is $3.15 (1 gallon of gas plus the bag of chips). If we put 2 gallons of gas in the car, the price is $5.05 (2 gallons of gas plus the bag of chips).<\/p>\n<p>We notice the pattern can be written as:\u00a0 <strong>price = $1.90 times the number of gallons<\/strong> <strong>plus $1.25<\/strong><\/p>\n<p>Using x and y, dropping the dollar sign, and using algebra notation, the pattern can be written as an equation:\u00a0\u00a0 <strong>y = 1.90x + 1.25<br \/>\n<\/strong><\/p>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Suppose gasoline is $2.10 per gallon. A customer also purchases a soda pop for $1.25. Write the equation that models this scenario, where x = the number of gallons of gasoline and y = the price the customer will pay.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q996665\">Show Answer<\/span><\/p>\n<div id=\"q996665\" class=\"hidden-answer\" style=\"display: none\">y = 2.10x + 1.25<\/div>\n<\/div>\n<\/div>\n<p>Let&#8217;s return to the model: <strong>y = 1.90x + 1.25<\/strong><\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05213127\/y-is-mx-plus-b.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5588 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/02\/05213127\/y-is-mx-plus-b-300x208.jpg\" alt=\"\" width=\"300\" height=\"208\" \/><\/a><\/p>\n<p>There are three <strong>terms<\/strong> in the model:<\/p>\n<ul>\n<li>y is the price the customer will pay<\/li>\n<li>1.90x tells us that for every gallon of gasoline put in the car, the customer will pay $1.90.<\/li>\n<li>1.25 is the constant part and does not vary.<\/li>\n<\/ul>\n<p>In some models, the constant term is called the <strong>initial amount <\/strong>or <strong>starting amount.<\/strong><\/p>\n<p>Consider the scenario of a student saving money to pay for tuition. Suppose the student was given $100 as birthday money. Then, the student saved $25 per week. Let y = total amount saved, and x = the number weeks since beginning to save, the model would be: <strong>y = 25x + 100.<\/strong><\/p>\n<p>The general model for saving money would be:<\/p>\n<p style=\"text-align: center;\"><strong>y = amount saved per week times the number of weeks plus the initial amount.<\/strong><\/p>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Suppose your friend was saving money to buy a car. She started with $400 and is now saving $75 per week from her part-time job. Let y = total amount saved, and x = the number of weeks since beginning to save. Write the equation that models this scenario.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q837084\">Show Answer<\/span><\/p>\n<div id=\"q837084\" class=\"hidden-answer\" style=\"display: none\">y = 75x + 400<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<p>To model scenarios involving linear growth, use y = mx + b.<\/p>\n<ul>\n<li>In algebra, <strong>m<\/strong> is called the <strong>slope<\/strong>.\n<ul>\n<li>In our models, m was the price per gallon, or amount saved per week.<\/li>\n<\/ul>\n<\/li>\n<li>In algebra, <strong>b<\/strong> is called the <strong>y-intercept<\/strong>.\n<ul>\n<li>In our models, b was the price of the snack purchased at the gas station, or the starting amount in a savings plan.<\/li>\n<\/ul>\n<\/li>\n<li>The term <strong>mx<\/strong> models the part of the scenario that changes (the variable part).<\/li>\n<li>The term <strong>b<\/strong> models the <strong>constant<\/strong> or <strong>fixed<\/strong> part of the scenario, which does not change.<\/li>\n<\/ul>\n<\/div>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>\n","protected":false},"author":359705,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5571","chapter","type-chapter","status-publish","hentry"],"part":356,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5571","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/359705"}],"version-history":[{"count":33,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5571\/revisions"}],"predecessor-version":[{"id":5573,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5571\/revisions\/5573"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/356"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/5571\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=5571"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=5571"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=5571"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=5571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}