{"id":680,"date":"2013-05-28T14:30:10","date_gmt":"2013-05-28T14:30:10","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=680"},"modified":"2026-03-25T10:52:09","modified_gmt":"2026-03-25T15:52:09","slug":"linear-equations","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/linear-equations\/","title":{"rendered":"Linear Equation Basics"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_fQ4maJoc41M\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_fQ4maJoc41M\" data-source-videoID=\"fQ4maJoc41M\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Linear Equation Basics Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Linear Equation Basics\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_fQ4maJoc41M:hover {cursor:pointer;} img#videoThumbnailImage_fQ4maJoc41M {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1638-linear-equation-basics-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_fQ4maJoc41M\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_fQ4maJoc41M\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Linear Equation Basics\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_fQ4maJoc41M\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_fQ4maJoc41M\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_fQ4maJoc41M\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction G2D_Function() {\n  var x = document.getElementById(\"G2D\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"G2D_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"G2D\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Determining_Linear_Equations\" class=\"smooth-scroll\">Determining Linear Equations<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#SlopeIntercept_Form\" class=\"smooth-scroll\">Slope-Intercept Form<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Linear_Equation_Practice_Questions\" class=\"smooth-scroll\">Linear Equation Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on linear equations! In this video we will look at:<\/p>\n<ul>\n<li>What linear equations are, and<\/li>\n<li>How to solve for different variables in a linear equation<\/li>\n<\/ul>\n<p>What exactly is a linear equation? Well, if you look at the word <em>linear<\/em> you can find the word <em>line<\/em>, so a linear equation is an equation for a line. Linear equations have two <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/identifying-variables\/\">variables<\/a>, most commonly \\(x\\) and \\(y\\), that are to a single degree, meaning they do not have variables to powers or roots. The equation \\(y = 9x + 5\\) is an example of a linear equation.<\/p>\n<h2><span id=\"Determining_Linear_Equations\" class=\"m-toc-anchor\"><\/span>Determining Linear Equations<\/h2>\n<p>\nLet\u2019s look at some equations and determine if they are linear. As each equation is shown, I want you to decide if it is linear or not.<\/p>\n<h3><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<div class=\"examplesentence\">\\(y = x^2 + 2\\)<\/div>\n<p>\n&nbsp;<br \/>\nNo, this is not a linear equation because the \\(x\\)-variable is squared.<\/p>\n<h3><span id=\"Example_2_1\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<div class=\"examplesentence\">\\(y = 4x + 1\\)<\/div>\n<p>\n&nbsp;<br \/>\nYes, this is a linear equation. There are two variables and they are both of a single degree.<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<div class=\"examplesentence\">\\(y + 3y = 7\\)<\/div>\n<p>\n&nbsp;<br \/>\nYes, even though this equation looks a little different from our other ones, it is still a linear equation because there are two variables and neither one has a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/roots\/\">root<\/a> or is raised to a power.<\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<div class=\"examplesentence\">\\(x = \\sqrt{y}-4\\)<\/div>\n<p>\n&nbsp;<br \/>\nNo, this is not a linear equation because of the square root.<\/p>\n<h2><span id=\"SlopeIntercept_Form\" class=\"m-toc-anchor\"><\/span>Slope-Intercept Form<\/h2>\n<p>\nThe most common way you will see linear equations is in the form \u201c\\(y=\\)\u201d because this is the easiest way to create a graph based on the equation. This is called slope-intercept form. However, it is still okay to have an equation with the \\(x\\)-variable, or both the \\(x\\)&#8211; and the \\(y\\)-variables, on the left side of the equation. <\/p>\n<h3><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s look at an equation that has the \\(x\\)-variable on the left side and rearrange it so it is in slope-intercept form.<\/p>\n<div class=\"examplesentence\">\\(x = 2y-7\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen we are looking for slope-intercept form, we want to get the \\(y\\)-variable by itself on the left side of the equation. To do this, we first have to add 7 to both sides.<\/p>\n<div class=\"examplesentence\">\\(x + 7 = 2y\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen we divide by 2 to get \\(y\\) by itself.<\/p>\n<div class=\"examplesentence\">\\(\\frac{x+7}{2} = y\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, dividing by 2 is the same as multiplying by \\(\\frac{1}{2}\\), so another way to write this equation is:<\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{2}x + \\frac{7}{2} = y\\)<\/div>\n<p>\n&nbsp;<br \/>\nAll that\u2019s left is to flip our equation around so the \\(y\\) is on the left side of the equation.<\/p>\n<div class=\"examplesentence\">\\(y = \\frac{1}{2}x + \\frac{7}{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we have our equation in slope-intercept form!<\/p>\n<h3><span id=\"Example_2_1\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s look at one more equation, but this time we are going to solve for \\(x\\).<\/p>\n<div class=\"examplesentence\">\\(6y \u2013 3x = 12\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur first step to get our \\(x\\)-variable by itself on the left side is to subtract \\(6y\\) from both sides of the equation.<\/p>\n<div class=\"examplesentence\">\\(-3x = 12 \u2013 6y\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, we divide the whole equation, which means both parts of the right-hand side of the equation, by -3.<\/p>\n<div class=\"examplesentence\">\\(x = -4 + 2y\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis is technically correct, but the best way to write an equation like this is to have the variable before the number so we are going to rearrange it to look like this.<\/p>\n<div class=\"examplesentence\">\\(x = 2y \u2013 4\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, the other way wasn\u2019t incorrect, but this is the more proper way to write our equation.<\/p>\n<hr>\n<p>\nI hope this overview of linear equations was helpful! Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you solve linear equations?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Solve linear equations by using the Order of Operations in reverse and use opposite operations on both sides of the equation to undo the operations until the variable is isolated.<\/p>\n<p>The order of operations is: parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right. To isolate a variable, work through this process backwards, starting with addition and subtraction and ending with parentheses.<\/p>\n<div class=\"lightbulb-example-2\" style=\"width: 70%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Solve \\(2(4x + 10) = -12\\)<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">Divide by 2 on both sides.<\/p>\n<p style=\"text-align:center;\">\\(4x + 10 = -6\\)<\/p>\n<p> Subtract 10 from both sides.<\/p>\n<p style=\"text-align:center;\">\\(4x = -16\\)<\/p>\n<p> Divide by 4 on both sides.<\/p>\n<p style=\"text-align:center; margin-bottom: 0em\">\\(x = -4\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you graph linear equations?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Graphing linear equations is typically done by plotting a point given in the equation, plotting a second point by using the slope, and drawing a straight line through the two points.<\/p>\n<p>Each form of an equation will have a different point to start with. Slope is rise over run, so to find your second point, move up (or down if there is a negative) the amount in the numerator and right the number in the denominator. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example (Point-Slope): \\((y &#8211; 3) = 4(x &#8211; 7)\\)<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">Plot the first point from the equation: \\((7,3)\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64581\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3.jpg\" alt=\"\" width=\"400\" height=\"391\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3-300x293.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3-1024x1002.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3-768x751.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-3-1536x1503.jpg 1536w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/p>\n<p> Plot the second point, found by using the slope \\((4,11)\\). The slope is 4, or \\(\\frac{4}{1}\\), so move up 4 and right 1.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64579\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4.jpg\" alt=\"\" width=\"400\" height=\"400\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4-300x300.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4-1024x1024.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4-150x150.jpg 150w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4-768x768.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-4-1536x1536.jpg 1536w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Draw a line through the two points:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64578\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5.jpg\" alt=\"\" width=\"400\" height=\"400\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5-300x300.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5-1024x1024.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5-150x150.jpg 150w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5-768x768.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-5-1536x1536.jpg 1536w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/div>\n\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example (Slope-Intercept): \\(y = -6x + 3\\)<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">Plot the first point from the equation (\\(y\\)-intercept): \\((0,3)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64587\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6.jpg\" alt=\"\" width=\"401\" height=\"392\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6-300x293.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6-1024x1002.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6-768x751.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-6-1536x1503.jpg 1536w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Plot the second point, found by using the slope: \\((1,-3)\\) \u2013 The slope is -6, or \\(\\frac{-6}{1}\\), so move down 6 and right 1.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64585\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1.jpg\" alt=\"\" width=\"400\" height=\"391\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1-300x293.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1-1024x1002.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1-768x751.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-1-1536x1503.jpg 1536w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Draw a line through the two points:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-64582\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2.jpg\" alt=\"\" width=\"400\" height=\"391\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2.jpg 1562w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2-300x293.jpg 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2-1024x1002.jpg 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2-768x751.jpg 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/Image-2-1536x1503.jpg 1536w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you solve linear equations with fractions?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Solve linear equations with a fraction multiplied by the variable by multiplying both sides by the reciprocal of the fraction. This makes the number in front of the variable a 1, so the fraction goes away. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Solve for \\(x\\text{: } \\dfrac{2}{3}x-7=29\\)<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">First, add 7 to both sides.<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{2}{3}x=36\\)<\/p>\n<p> Then, multiply by the reciprocal of the fraction (\\(\\frac{3}{2}\\)). <\/p>\n<p style=\"text-align:center;\">\\((\\dfrac{3}{2})(\\dfrac{2}{3})x=36(\\dfrac{3}{2})\\)<\/p>\n<p> <\/p>\n<p style=\"text-align:center; margin-bottom: 0em;\">\\(x=54\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Linear_Equation_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Linear Equation Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is \\(-3x+2y=12\\) in slope-intercept form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(y=-\\frac{2}{3}x+6\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(y=\\frac{2}{3}x+6\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(y=-\\frac{3}{2}x+6\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">\\(y=\\frac{3}{2}x+6\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The slope-intercept form is when the equation looks like \\(y=mx+b\\), where the slope and \\(y\\)-intercept are visible in the equation. To change the equation from standard form to slope-intercept form, we solve the equation for \\(y\\).<\/p>\n<div style=\"text-align:center;\">\n<p style=\"margin-bottom: 18px\">\\(-3x+2y=12\\)<\/p>\n<p style=\"margin-bottom: 24px\">\\(2y=3x+12\\)<\/p>\n<p style=\"margin-bottom: 18px; font-size: 120%\">\\(\\frac{2y}{2}=\\frac{3x}{2}+\\frac{12}{2}\\)<\/p>\n<p>\\(y=\\frac{3}{2}x+6\\)\n<\/p><\/div>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich is a linear equation?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(y=\\sqrt{x}-4\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\\(y=\\frac{1}{2}x+5\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(y=2x^2+1\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(y=-x^3-6\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Since the definition of a linear equation is an equation of a line where the \\(x\\)-term and \\(y\\)-term are raised to a single degree, the equation \\(y=\\frac{1}{2}x+5\\), is the only equation that meets this requirement. Therefore, it is a linear equation.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich shows \\(x=-\\frac{1}{3}y-3\\) in slope-intercept form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(y=-\\frac{1}{3}x-6\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(y=-\\frac{1}{3}x+6\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\(y=-3x-9\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(y=-3x+9\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The slope-intercept form of an equation is the equation in terms of \\(y\\). We will solve the equation until \\(y\\) is isolated on one side.<\/p>\n<div style=\"text-align:center;\">\n<p style=\"margin-bottom: 18px\">\\(x=-\\frac{1}{3}y-3\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(x+3=-\\frac{1}{3}y\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(-3(x+3=-\\frac{1}{3}y)\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(-3x-9=y\\)<\/p>\n<p>\\(y=-3x-9\\)\n<\/p><\/div>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is \\(5x\u20134y=20\\) in terms of \\(x\\)? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(x=-\\frac{4}{5}y+4\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">\\(x=\\frac{4}{5}y+4\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(x=-\\frac{5}{4}y+4\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(x=\\frac{5}{4}y+4\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To put an equation in terms of \\(x\\) means we solve the equation to have \\(x\\) isolated on one side. To do that we will use our algebra skills.<\/p>\n<div style=\"text-align:center;\">\n<p style=\"margin-bottom: 18px\">\\(5x\u20134y=20\\)<\/p>\n<p style=\"margin-bottom: 23px\">\\(5x=4y+20\\)<\/p>\n<p style=\"margin-bottom: 18px; font-size: 120%\">\\(\\frac{5x}{5}=\\frac{4y}{5}+\\frac{20}{5}\\)<\/p>\n<p>\\(x=\\frac{4}{5}y+4\\)\n<\/p><\/div>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is \\(y=\\frac{1}{3}x-5\\) in terms of \\(x\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x=y+15\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(x=y-15\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(x=3y+15\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x=3y-15\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Writing an equation in terms of \\(x\\) means we need to isolate the variable \\(x\\) on one side of the equation.<\/p>\n<div style=\"text-align:center;\">\n<p style=\"margin-bottom: 18px\">\\(y=\\frac{1}{3}x-5\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(y+5=\\frac{1}{3}x\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(3(y+5=\\frac{1}{3}x)\\)<\/p>\n<p style=\"margin-bottom: 18px\">\\(3y+15=x\\)<\/p>\n<p>\\(x=3y+15\\)\n<\/p><\/div>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":100618,"parent":0,"menu_order":32,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-680","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-linear-equations-videos-algebra-ii-videos","7":"page_category-linear-equations-videos","8":"page_category-math-advertising-group","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/680","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=680"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/680\/revisions"}],"predecessor-version":[{"id":278974,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/680\/revisions\/278974"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100618"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}