{"id":2865,"date":"2024-02-09T19:45:54","date_gmt":"2024-02-09T19:45:54","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=2865"},"modified":"2026-03-10T16:28:07","modified_gmt":"2026-03-10T16:28:07","slug":"7-1-definition-of-linear-equations-in-two-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/7-1-definition-of-linear-equations-in-two-variables\/","title":{"raw":"7.2 Definition of Linear Equations in Two Variables","rendered":"7.2 Definition of Linear Equations in Two Variables"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h1>Learning Objectives<\/h1>\r\n<ul>\r\n \t<li>Define a linear equation<\/li>\r\n \t<li>Determine if an equation in two variables is linear<\/li>\r\n \t<li>Write a linear equation in standard form<\/li>\r\n \t<li>Write a linear equation in slope-intercept form<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h1>Key words<\/h1>\r\n<ul>\r\n \t<li><strong>Linear equation<\/strong>: an equation where each term has only one variable and the highest exponent of each variable is 1<\/li>\r\n \t<li><strong>Standard form<\/strong>: [latex]ax+by=c[\/latex] where [latex]a,\\,b,\\,c[\/latex] are constants<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Definition of Linear Equations<\/h2>\r\nA linear equation is an equation with the combination of a constant and one or more variable terms. Each variable term contains only one variable, and the exponent of the variable is one.\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLES<\/h3>\r\n<ul>\r\n \t<li>[latex] 2x+3=5x-4 [\/latex] is a linear equation in one variable<\/li>\r\n \t<li>[latex] 2x+3y=5 [\/latex] is a linear equation in two variables<\/li>\r\n \t<li>[latex] 5x-3y+2z=12 [\/latex]\u00a0is a linear equation in three variables<\/li>\r\n \t<li>[latex] a_{1}x_{1}+a_{2}x_{2} + ... + a_{n}x_{n} = c [\/latex] is the general form of a linear equation<\/li>\r\n<\/ul>\r\n<\/div>\r\nRemember that if a variable is in the denominator with an exponent of 1, it really has an exponent of \u20131. For example, [latex]\\frac{1}{x}=x^{-1}[\/latex]. Therefore, for a variable to have an exponent of 1, it is always in the numerator.\r\n<h2>Linear Equations in Two Variables<\/h2>\r\nA linear equation in two variables is a linear equation with two variables where the exponents on the variables are 1 and each term contains only one variable.\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLE<\/h3>\r\nThe following are examples of two-variable linear equations:\r\n<ul>\r\n \t<li>[latex]3x + 5y = 7[\/latex]<\/li>\r\n \t<li>[latex]y = \\frac{2}{3}x - 3[\/latex]<\/li>\r\n \t<li>[latex]\\left(y-2\\right)=\\frac{-2}{7}\\left(x+3\\right)[\/latex]<\/li>\r\n<\/ul>\r\nThe following are NOT two-variable linear equations:\r\n<ul>\r\n \t<li>[latex]x^2 + y^2 = 9[\/latex]\r\n<ul>\r\n \t<li>This equation is not linear because the exponent of the [latex]x[\/latex] and [latex]y[\/latex]-variables is not 1.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>[latex]\\sqrt{2x-3}=y[\/latex]\r\n<ul>\r\n \t<li>This equation is not linear because the exponent on the [latex]x[\/latex]-variable is not 1.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>[latex]\\frac{2}{x}=3y[\/latex]\r\n<ul>\r\n \t<li>This equation is not linear because the exponent on the [latex]x[\/latex]-variable is not 1. (it is -1)<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe <em><strong>standard form\u00a0<\/strong><\/em>of a linear equation in two variable is: [latex]ax+by=c[\/latex] where [latex]a,\\,b,\\,c[\/latex] are constants.\r\n\r\nFor example the equation\u00a0[latex] 2x+y = 5 [\/latex] is a two-variable linear equation written in standard form.\r\n\r\nLinear equations are not always given in standard form but can always be simplified to standard form using the addition and multiplication properties of equality.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nDetermine if the equation is linear and is in standard form. If it is not, rewrite it in standard form.\r\n<ol>\r\n \t<li>[latex]3x-4y=9[\/latex]<\/li>\r\n \t<li>[latex]y=x+6[\/latex]<\/li>\r\n \t<li>[latex]4x+6y-9=0[\/latex]<\/li>\r\n \t<li>[latex]3xy=8[\/latex]<\/li>\r\n \t<li>[latex]3(x-2)+5y=12[\/latex]<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n1. [latex]3x-4y=9[\/latex] is in the form [latex]ax+by=c[\/latex] so is in standard form.\r\n\r\n&nbsp;\r\n\r\n2. [latex]y=x+6[\/latex] is a linear equation but is not in standard form. To write it in standard form, all the variables must be on the same side, so we will subtract [latex]x[\/latex] from both sides of the equation:\u00a0\u00a0[latex]\\begin{equation}\\begin{aligned}y=x+6 \\\\ y-x=6\\end{aligned}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3. [latex]4x+6y-9=0[\/latex] is a linear\u00a0equation but is not in standard form. We need to add [latex]9[\/latex] to both sides of the equation:\u00a0\u00a0[latex]\\begin{equation}\\begin{aligned}4x+6y-9=0 \\\\ 4x+6y=9\\end{aligned}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4. [latex]3xy=8[\/latex] is not a linear equation. Although each exponent on the variables is 1, there is more than one variable in the term [latex]3xy[\/latex].\r\n\r\n&nbsp;\r\n\r\n5. [latex]3(x-2)+5y=12[\/latex] is a linear equation but is not in standard form. We need to distribute and add [latex]6[\/latex] to both sides:\r\n<p style=\"text-align: center;\">\u00a0[latex]\\begin{equation}\\begin{aligned}3(x-2)+5y=12 \\\\ 3x-6+5y=12 \\\\ 3x+5y=18\\end{aligned}\\end{equation}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nWrite the linear equation in standard form.\r\n<ol>\r\n \t<li>[latex]y=-3x+6[\/latex]<\/li>\r\n \t<li>[latex]2x+y-9=0[\/latex]<\/li>\r\n \t<li>[latex]3(2x-1)-7y=4[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"hjm410\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"hjm410\"]\r\n<ol>\r\n \t<li>[latex]3x+y=6[\/latex]<\/li>\r\n \t<li>[latex]2x+y=9[\/latex]<\/li>\r\n \t<li>[latex]6x-7y=7[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nAnother way to write a linear equation in two variables is called <em><strong>slope-intercept form<\/strong><\/em>. Slope-Intercept form: [latex]y=mx+b [\/latex] where [latex]m[\/latex] and [latex]b[\/latex] are constants. We will find out later exactly what these constants represent. For example [latex]y=3x-6[\/latex] and [latex]y=-\\frac{2}{3}x+\\frac{4}{5}[\/latex] are linear equations in slope-intercept form.\r\n\r\nIf the linear equation is not given in slope-intercept form we can always rearrange it using the addition and multiplication properties of equality.\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\nWrite the linear equations in slope-intercept form.\r\n<ol>\r\n \t<li>[latex]2x+y=7[\/latex]<\/li>\r\n \t<li>[latex]x-3y=6[\/latex]<\/li>\r\n \t<li>[latex]2x-5y=4[\/latex]<\/li>\r\n \t<li>[latex]2(x-3)-(2y-1)=1[\/latex]<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n1.\r\n\r\n[latex]\\begin{equation}\\begin{aligned}2x+y &amp; =7 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract }2x\\text{ from both sides} \\\\ y &amp; =-2x+7\\end{aligned}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2.\r\n\r\n[latex]\\begin{equation}\\begin{aligned}x-3y &amp; =6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract }\\;x\\text { from both sides}\\\\ -3y &amp; =-x+6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide both sides by }-3 \\\\ y &amp; =\\frac{-x+6}{-3} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute the }-3 \\\\ y &amp; =\\frac{1}{3}x-2\\end{aligned}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n\r\n3.\r\n\r\n[latex]\\begin{equation}\\begin{aligned}2x-5y &amp; =4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract } \\;2x \\\\-5y &amp; =-2x+4\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide by }-5 \\\\y &amp; = \\frac{-2x+4}{-5}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\ y &amp; =\\frac{2}{5}x-\\frac{4}{5}\\end{aligned}\\end{equation}[\/latex]\r\n\r\n&nbsp;\r\n\r\n4.\r\n\r\n[latex]\\begin{equation}\\begin{aligned}2(x-3)-(2y-1) &amp; =1\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\2x-6-2y+1 &amp; =1 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Simplify} \\\\ 2x-2y-5 &amp; =1 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Add } 5 \\\\ 2x-2y &amp; =6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract}\\;2x \\\\-2y &amp; = -2x+6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide by}\\; -2 \\\\ y &amp; = \\frac{-2x+6}{-2} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\ y &amp; =x-3 \\end{aligned}\\end{equation}[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nWrite the linear equations in slope-intercept form.\r\n<ol>\r\n \t<li>[latex]x+4y=8[\/latex]<\/li>\r\n \t<li>[latex]3x+2y=4[\/latex]<\/li>\r\n \t<li>[latex]2(x+4)-(y-3)=2[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"hjm799\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"hjm799\"]\r\n<ol>\r\n \t<li>[latex]y=-\\frac{1}{4}x+2[\/latex]<\/li>\r\n \t<li>[latex]y=-\\frac{3}{2}x+2[\/latex]<\/li>\r\n \t<li>[latex]y=2x+9[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h1>Learning Objectives<\/h1>\n<ul>\n<li>Define a linear equation<\/li>\n<li>Determine if an equation in two variables is linear<\/li>\n<li>Write a linear equation in standard form<\/li>\n<li>Write a linear equation in slope-intercept form<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h1>Key words<\/h1>\n<ul>\n<li><strong>Linear equation<\/strong>: an equation where each term has only one variable and the highest exponent of each variable is 1<\/li>\n<li><strong>Standard form<\/strong>: [latex]ax+by=c[\/latex] where [latex]a,\\,b,\\,c[\/latex] are constants<\/li>\n<\/ul>\n<\/div>\n<h2>Definition of Linear Equations<\/h2>\n<p>A linear equation is an equation with the combination of a constant and one or more variable terms. Each variable term contains only one variable, and the exponent of the variable is one.<\/p>\n<div class=\"textbox exercises\">\n<h3>ExAMPLES<\/h3>\n<ul>\n<li>[latex]2x+3=5x-4[\/latex] is a linear equation in one variable<\/li>\n<li>[latex]2x+3y=5[\/latex] is a linear equation in two variables<\/li>\n<li>[latex]5x-3y+2z=12[\/latex]\u00a0is a linear equation in three variables<\/li>\n<li>[latex]a_{1}x_{1}+a_{2}x_{2} + ... + a_{n}x_{n} = c[\/latex] is the general form of a linear equation<\/li>\n<\/ul>\n<\/div>\n<p>Remember that if a variable is in the denominator with an exponent of 1, it really has an exponent of \u20131. For example, [latex]\\frac{1}{x}=x^{-1}[\/latex]. Therefore, for a variable to have an exponent of 1, it is always in the numerator.<\/p>\n<h2>Linear Equations in Two Variables<\/h2>\n<p>A linear equation in two variables is a linear equation with two variables where the exponents on the variables are 1 and each term contains only one variable.<\/p>\n<div class=\"textbox exercises\">\n<h3>ExAMPLE<\/h3>\n<p>The following are examples of two-variable linear equations:<\/p>\n<ul>\n<li>[latex]3x + 5y = 7[\/latex]<\/li>\n<li>[latex]y = \\frac{2}{3}x - 3[\/latex]<\/li>\n<li>[latex]\\left(y-2\\right)=\\frac{-2}{7}\\left(x+3\\right)[\/latex]<\/li>\n<\/ul>\n<p>The following are NOT two-variable linear equations:<\/p>\n<ul>\n<li>[latex]x^2 + y^2 = 9[\/latex]\n<ul>\n<li>This equation is not linear because the exponent of the [latex]x[\/latex] and [latex]y[\/latex]-variables is not 1.<\/li>\n<\/ul>\n<\/li>\n<li>[latex]\\sqrt{2x-3}=y[\/latex]\n<ul>\n<li>This equation is not linear because the exponent on the [latex]x[\/latex]-variable is not 1.<\/li>\n<\/ul>\n<\/li>\n<li>[latex]\\frac{2}{x}=3y[\/latex]\n<ul>\n<li>This equation is not linear because the exponent on the [latex]x[\/latex]-variable is not 1. (it is -1)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<p>The <em><strong>standard form\u00a0<\/strong><\/em>of a linear equation in two variable is: [latex]ax+by=c[\/latex] where [latex]a,\\,b,\\,c[\/latex] are constants.<\/p>\n<p>For example the equation\u00a0[latex]2x+y = 5[\/latex] is a two-variable linear equation written in standard form.<\/p>\n<p>Linear equations are not always given in standard form but can always be simplified to standard form using the addition and multiplication properties of equality.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Determine if the equation is linear and is in standard form. If it is not, rewrite it in standard form.<\/p>\n<ol>\n<li>[latex]3x-4y=9[\/latex]<\/li>\n<li>[latex]y=x+6[\/latex]<\/li>\n<li>[latex]4x+6y-9=0[\/latex]<\/li>\n<li>[latex]3xy=8[\/latex]<\/li>\n<li>[latex]3(x-2)+5y=12[\/latex]<\/li>\n<\/ol>\n<h4>Solution<\/h4>\n<p>1. [latex]3x-4y=9[\/latex] is in the form [latex]ax+by=c[\/latex] so is in standard form.<\/p>\n<p>&nbsp;<\/p>\n<p>2. [latex]y=x+6[\/latex] is a linear equation but is not in standard form. To write it in standard form, all the variables must be on the same side, so we will subtract [latex]x[\/latex] from both sides of the equation:\u00a0\u00a0[latex]\\begin{equation}\\begin{aligned}y=x+6 \\\\ y-x=6\\end{aligned}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3. [latex]4x+6y-9=0[\/latex] is a linear\u00a0equation but is not in standard form. We need to add [latex]9[\/latex] to both sides of the equation:\u00a0\u00a0[latex]\\begin{equation}\\begin{aligned}4x+6y-9=0 \\\\ 4x+6y=9\\end{aligned}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4. [latex]3xy=8[\/latex] is not a linear equation. Although each exponent on the variables is 1, there is more than one variable in the term [latex]3xy[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<p>5. [latex]3(x-2)+5y=12[\/latex] is a linear equation but is not in standard form. We need to distribute and add [latex]6[\/latex] to both sides:<\/p>\n<p style=\"text-align: center;\">\u00a0[latex]\\begin{equation}\\begin{aligned}3(x-2)+5y=12 \\\\ 3x-6+5y=12 \\\\ 3x+5y=18\\end{aligned}\\end{equation}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Write the linear equation in standard form.<\/p>\n<ol>\n<li>[latex]y=-3x+6[\/latex]<\/li>\n<li>[latex]2x+y-9=0[\/latex]<\/li>\n<li>[latex]3(2x-1)-7y=4[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"qhjm410\">Show Answer<\/span><\/p>\n<div id=\"qhjm410\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]3x+y=6[\/latex]<\/li>\n<li>[latex]2x+y=9[\/latex]<\/li>\n<li>[latex]6x-7y=7[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Another way to write a linear equation in two variables is called <em><strong>slope-intercept form<\/strong><\/em>. Slope-Intercept form: [latex]y=mx+b[\/latex] where [latex]m[\/latex] and [latex]b[\/latex] are constants. We will find out later exactly what these constants represent. For example [latex]y=3x-6[\/latex] and [latex]y=-\\frac{2}{3}x+\\frac{4}{5}[\/latex] are linear equations in slope-intercept form.<\/p>\n<p>If the linear equation is not given in slope-intercept form we can always rearrange it using the addition and multiplication properties of equality.<\/p>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>Write the linear equations in slope-intercept form.<\/p>\n<ol>\n<li>[latex]2x+y=7[\/latex]<\/li>\n<li>[latex]x-3y=6[\/latex]<\/li>\n<li>[latex]2x-5y=4[\/latex]<\/li>\n<li>[latex]2(x-3)-(2y-1)=1[\/latex]<\/li>\n<\/ol>\n<h4>Solution<\/h4>\n<p>1.<\/p>\n<p>[latex]\\begin{equation}\\begin{aligned}2x+y & =7 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract }2x\\text{ from both sides} \\\\ y & =-2x+7\\end{aligned}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2.<\/p>\n<p>[latex]\\begin{equation}\\begin{aligned}x-3y & =6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract }\\;x\\text { from both sides}\\\\ -3y & =-x+6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide both sides by }-3 \\\\ y & =\\frac{-x+6}{-3} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute the }-3 \\\\ y & =\\frac{1}{3}x-2\\end{aligned}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>3.<\/p>\n<p>[latex]\\begin{equation}\\begin{aligned}2x-5y & =4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract } \\;2x \\\\-5y & =-2x+4\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide by }-5 \\\\y & = \\frac{-2x+4}{-5}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\ y & =\\frac{2}{5}x-\\frac{4}{5}\\end{aligned}\\end{equation}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>4.<\/p>\n<p>[latex]\\begin{equation}\\begin{aligned}2(x-3)-(2y-1) & =1\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\2x-6-2y+1 & =1 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Simplify} \\\\ 2x-2y-5 & =1 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Add } 5 \\\\ 2x-2y & =6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Subtract}\\;2x \\\\-2y & = -2x+6 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Divide by}\\; -2 \\\\ y & = \\frac{-2x+6}{-2} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{Distribute} \\\\ y & =x-3 \\end{aligned}\\end{equation}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Write the linear equations in slope-intercept form.<\/p>\n<ol>\n<li>[latex]x+4y=8[\/latex]<\/li>\n<li>[latex]3x+2y=4[\/latex]<\/li>\n<li>[latex]2(x+4)-(y-3)=2[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"qhjm799\">Show Answer<\/span><\/p>\n<div id=\"qhjm799\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]y=-\\frac{1}{4}x+2[\/latex]<\/li>\n<li>[latex]y=-\\frac{3}{2}x+2[\/latex]<\/li>\n<li>[latex]y=2x+9[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"author":370291,"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-2865","chapter","type-chapter","status-publish","hentry"],"part":2860,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/2865","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/users\/370291"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/2865\/revisions"}],"predecessor-version":[{"id":3088,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/2865\/revisions\/3088"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/parts\/2860"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/2865\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/media?parent=2865"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=2865"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/contributor?post=2865"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/license?post=2865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}