{"id":684,"date":"2013-05-28T14:31:56","date_gmt":"2013-05-28T14:31:56","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=684"},"modified":"2026-03-26T11:59:24","modified_gmt":"2026-03-26T16:59:24","slug":"slope-intercept-and-point-slope-forms","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/slope-intercept-and-point-slope-forms\/","title":{"rendered":"Slope-Intercept and Point-Slope Forms"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_br4ZW_XuQcY\" 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_br4ZW_XuQcY\" data-source-videoID=\"br4ZW_XuQcY\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Slope-Intercept and Point-Slope Forms Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Slope-Intercept and Point-Slope Forms\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_br4ZW_XuQcY:hover {cursor:pointer;} img#videoThumbnailImage_br4ZW_XuQcY {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/693-slope-intercept-and-point-slope-forms-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_br4ZW_XuQcY\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_br4ZW_XuQcY\" 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\",\"Slope-Intercept and Point-Slope Forms\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_br4ZW_XuQcY\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_br4ZW_XuQcY\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_br4ZW_XuQcY\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction myq_Function() {\n  var x = document.getElementById(\"myq\");\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=\"myq_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=\"myq\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Standard_Form\" class=\"smooth-scroll\">Standard Form<\/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=\"#Converting_Between_Forms\" class=\"smooth-scroll\">Converting Between Forms<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Slope_Example_Problems\" class=\"smooth-scroll\">Slope Example Problems<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Graphing_from_the_YIntercept\" class=\"smooth-scroll\">Graphing from the Y-Intercept<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#PointSlope_Form\" class=\"smooth-scroll\">Point-Slope 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=\"#SlopeIntercept_and_PointSlope_Practice_Questions\" class=\"smooth-scroll\">Slope-Intercept and Point-Slope 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>Hi, and welcome to this review of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/linear-equations\/\">linear equation<\/a> forms! Specifically, we\u2019ll be talking about slope-intercept and point-slope forms. We will also review the terminology and the process of graphing linear equations in these forms. Let\u2019s get started!<\/p>\n<p>A linear equation can be expressed in many different ways, but no matter which form you use, it just represents a straight line. <\/p>\n<h2><span id=\"Standard_Form\" class=\"m-toc-anchor\"><\/span>Standard Form<\/h2>\n<p>\nThe standard form of a linear equation is written as: \\(Ax +By=C\\), where \\(A\\), \\(B\\), and \\(C\\) are constants, and \\(x\\) and \\(y\\) represent variables. This form of the equation is very useful for some purposes in math.<\/p>\n<p>For example, a line can be quickly graphed when it is in this form by finding the \\(x\\)&#8211; and \\(y\\)-intercepts. There are also methods of solving systems of equations that require each equation in the system to be written in this form.<\/p>\n<h2><span id=\"SlopeIntercept_Form\" class=\"m-toc-anchor\"><\/span>Slope-Intercept Form<\/h2>\n<p>\nRearranging the standard form equation into slope-intercept form, \\(y=mx + b\\), reveals other key features of the line, namely, the slope and the \\(y\\)-intercept. The <strong>slope<\/strong> of a line describes the slant, or steepness, and the \\(y\\)-intercept is the point on the graph where the line crosses the \\(y\\)-axis. <\/p>\n<p>Notationally, slope is represented by \\(m\\) and the \\(y\\)-intercept is represented by \\(b\\). Because the \\(y\\)-intercept is an actual point on the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/cartesian-coordinate-plane-and-graphing\/\">coordinate plane<\/a>, it is represented as an ordered pair, \\((0,b)\\).<\/p>\n<h2><span id=\"Converting_Between_Forms\" class=\"m-toc-anchor\"><\/span>Converting Between Forms<\/h2>\n<p>\nSometimes you will be asked to rearrange an equation from one form to another. Here\u2019s an example:<\/p>\n<div class=\"examplesentence\">\\(2x+3y=12\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, the standard form of a linear equation is \\(Ax +By=C\\), so this is currently in standard form. If we want to change it to slope-intercept form, we are going to need to rearrange it so that \\(y\\) is by itself our the left side.<\/p>\n<p>Our first step is to subtract \\(2x\\) from both sides.<\/p>\n<p>\\(3y=12-2x\\) is what we have now.<\/p>\n<p>Then, we\u2019re going to divide everything by 3, which gives us \\(y=4- \\frac{2}{3}x\\).<\/p>\n<p>This is almost right, but if we look again at slope-intercept form we see that we need the \\(x\\)-term to be in front. Thankfully we can think of this as \\(4+(- \\frac{2}{3}x)\\) and use the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/associative-property\/\">commutative property of addition<\/a> to swap their places. This gives us:<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(y=-\\frac{2}{3}x+4\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>The resulting equation is more informative about the line than the original equation in standard form. The coefficient of \\(x\\), \\(-\\frac{2}{3}\\), is the slope. A negative slope tells us that the line slants downward, from left to right. The \\(y\\)-intercept of 4 tells us that the line crosses the \\(y\\)-axis at the point \\((0,4)\\). <\/p>\n<h2><span id=\"Slope_Example_Problems\" class=\"m-toc-anchor\"><\/span>Slope Example Problems<\/h2>\n<p>\nNow that we have seen how to convert a standard form equation into slope-intercept form, let\u2019s practice recognizing the key features of slope and the \\(y\\)-intercept with a few examples.<\/p>\n<p>For these examples, we want to name the slope, describe the slant of the line, and name the \\(y\\)-intercept as an ordered pair.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<div class=\"examplesentence\">\\(y=2x+3\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe slope of this equation is \\(m=2\\), the coefficient of the \\(x\\)-variable. A positive slope indicates that the line slants upward from left to right. The \\(y\\)-intercept is \\(b=3\\), which indicates that the line crosses the \\(y\\)-axis at the point, \\((0,3)\\).<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another one:<\/p>\n<div class=\"examplesentence\">\\(y=\\frac{3}{5}x-\\frac{2}{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe slope of this equation is \\(m=\\frac{3}{5}\\). Because the slope is positive, the line slants upward from left to right. The \\(y\\)-intercept is \\(b=-\\frac{2}{3}\\), which indicates that the line crosses the \\(y\\)-axis at the point, \\((0,-\\frac{2}{3})\\).<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nLet\u2019s try one more:<\/p>\n<div class=\"examplesentence\">\\(y= -5x-2\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe slope is \\(m=-5\\). Negative slope means that the line slants downward from left to right; the line crosses the \\(y\\)-axis at the point \\((0,-2)\\).<\/p>\n<h2><span id=\"Graphing_from_the_YIntercept\" class=\"m-toc-anchor\"><\/span>Graphing from the Y-Intercept<\/h2>\n<p>\nAs you can imagine, knowing where the line crosses the \\(y\\)-axis and the slope of the line will make the line very easy to graph. Now, let\u2019s take a look at how slope provides you with instructions to graph from the \\(y\\)-intercept.<\/p>\n<p>Any value of slope can be looked at as a fraction, where the numerator indicates where to move along the \\(y\\)-axis, and the denominator indicates where to move along the \\(x\\)-axis. <\/p>\n<div class=\"examplesentence\" style=\"font-size: 115%;\">\\(\\text{Slope}=\\frac{\\text{Vertical Change}}{\\text{Horizontal Change}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nMovement along the \\(y\\)-axis is typically referred to as the \u201crise.\u201d A <strong>positive rise<\/strong> value would instruct a move up the \\(y\\)-axis, while a <strong>negative rise<\/strong> would indicate a move down the \\(y\\)-axis. Likewise, a <strong>positive run<\/strong> value would mean a shift to the right, and a <strong>negative run<\/strong> would mean a shift to the left.<\/p>\n<h3><span id=\"Rise_and_Run_Examples\" class=\"m-toc-anchor\"><\/span>Rise and Run Examples<\/h3>\n<p>\nHere are a few examples to practice identifying the rise and run indicated by a given slope:<\/p>\n<h4 style=\"margin-bottom: 0.5em; text-transform: uppercase;\"><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h4>\n<div class=\"examplesentence\">\\(m=5\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis slope is not written as a fraction, but any whole number can be rewritten as a fraction over 1:<\/p>\n<div class=\"examplesentence\">\\(m=\\frac{5}{1}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe numerator, 5, is the rise. Positive value means UP, 5. The denominator is the run. Positive value means RIGHT, 1. <\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_2_1\" class=\"m-toc-anchor\"><\/span>Example #2<\/h4>\n<p>\nLet\u2019s try another one.<\/p>\n<div class=\"examplesentence\">\\(m=\\frac{-2}{3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen you have a negative slope, you can consider either the numerator <em>or<\/em> the denominator to be negative, not both! For this example, let\u2019s consider the numerator, the rise, to be the negative value.<\/p>\n<p>Negative value means DOWN, 2. The denominator, 3, is the run. Positive value means RIGHT, 3. <\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_3_2\" class=\"m-toc-anchor\"><\/span>Example #3<\/h4>\n<p>\nHere\u2019s one last example:<\/p>\n<div class=\"examplesentence\">\\(m= &#8211; 3\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, we need to rewrite the whole number as a fraction: \\(m=-\\frac{3}{1}\\). Let the numerator be the negative value. Rise is -3, DOWN, 3. Run is 1, RIGHT, 1.<\/p>\n<h3><span id=\"Graphing_Examples\" class=\"m-toc-anchor\"><\/span>Graphing Examples<\/h3>\n<p>\nNow onto some graphing. People sometimes find it helpful to use the notation of slope-intercept form to get started. &#8220;<strong>B<\/strong>egin&#8221; at <strong>\\(b\\)<\/strong>, and &#8220;<strong>M<\/strong>ove&#8221; according to <strong>\\(m\\)<\/strong>. <\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_1_2\" class=\"m-toc-anchor\"><\/span>Example #1<\/h4>\n<p>\nLet\u2019s graph the linear equation in slope-intercept form:<\/p>\n<div class=\"examplesentence\">\\(y= \\frac{2}{3}x-2\\)<\/div>\n<p>\n&nbsp;<br \/>\n<strong>Step 1<\/strong>: <strong>B<\/strong>egin at <strong>\\(b\\)<\/strong><br \/>\nPlot the \\(y\\)-intercept, \\((0,-2)\\), 1st point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65122\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1.png\" alt=\"plot the first point\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-1-1-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 2<\/strong>: <strong>M<\/strong>ove by \\(m=\\frac{2}{3}\\)<br \/>\nRise equals UP, 2.<br \/>\nRun equals RIGHT, 3.<br \/>\nPlot the 2nd point at \\((3,0)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65125\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2.png\" alt=\"move by m=2\/3\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-2-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 3<\/strong>: Repeat.<br \/>\nRise equals UP, 2<br \/>\nRun equals RIGHT, 3<br \/>\nPlot the 3rd point at \\((6,2)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65126\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3.png\" alt=\"repeat move by m=2\/3\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-3-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p><strong>Step 4<\/strong>: Draw a straight line through the three points. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65129\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4.png\" alt=\"draw a line through the points\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-4-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p>Got the hang of it? Let\u2019s try one more:<\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_2_1\" class=\"m-toc-anchor\"><\/span>Example #2<\/h4>\n<div class=\"examplesentence\">\\(y=-2x-3\\)<\/div>\n<p>\n&nbsp;<br \/>\n<strong>Step 1<\/strong>: <strong>B<\/strong>egin at <strong>\\(b\\)<\/strong>, <br \/>\nPlot the \\(y\\)-intercept, \\((0,-3)\\), 1st point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65131\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5.png\" alt=\"plot the first point (5)\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-5-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/>  <\/p>\n<p><strong>Step 2<\/strong>: <strong>M<\/strong>ove by \\(m=-\\frac{2}{1}\\). (Let the rise be negative!)<br \/>\nRise equals DOWN, 2<br \/>\nRun equals RIGHT, 1<br \/>\nPlot the 2nd point at \\((1, -5)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65104\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6.png\" alt=\"move by the slope -2\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-6-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p><strong>Step 3<\/strong>: Repeat. <br \/>\nRise equals DOWN, 2<br \/>\nRun equals RIGHT, 1<br \/>\nPlot the 3rd point at \\((2, -7)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65107\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7.png\" alt=\"repeat moving by the slope -2\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-7-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 4<\/strong>: Draw a straight line through the three points. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65110\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8.png\" alt=\"draw a straight line through the points\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/IMAGE-8-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p>Note the slant downward, from left to right, due to the negative slope in this equation.<\/p>\n<h2><span id=\"PointSlope_Form\" class=\"m-toc-anchor\"><\/span>Point-Slope Form<\/h2>\n<p>\nNow that we have had some review of the key features of linear equations, we have the tools to explore the <strong>point-slope form<\/strong>. This form is of special use if we know one point that is on the line, and the slope. The general form of this arrangement is \\(y-y_{1}=m(x-x_{1})\\), where \\(m=\\text{slope}\\) and \\((x_{1},y_{1})\\) is another point that is known on the line.<\/p>\n<p>Using this template, let\u2019s practice identifying the slope and the point from the following examples of point-slope form:<\/p>\n<h4 style=\"margin-bottom: 0.5em; text-transform: uppercase;\"><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h4>\n<div class=\"examplesentence\">\\(y-5=3(x-2)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis is a straightforward example. First, identify the slope as the coefficient outside the parentheses, \\(m=3\\). When naming the point on the line, note that in the general form the \\(x\\)-coordinate is being subtracted from \\(x\\), and the \\(y\\)-coordinate is being subtracted from \\(y\\), so the ordered pair of the point will be \\((2,5)\\). <\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_2_1\" class=\"m-toc-anchor\"><\/span>Example #2<\/h4>\n<p>\nHere\u2019s another one:<\/p>\n<div class=\"examplesentence\">\\(y+3=-\\frac{1}{2}(x-4)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe slope in this equation is \\(m=-\\frac{1}{2}\\). <\/p>\n<p>How is this equation different from the general form \\(y-y_{1}=m(x-x_{1})\\)? You may have noticed that the \\(y\\)-value of the point, 3, is being added. <\/p>\n<p>To identify the point that is on this line, the equation must look like the general form, which subtracts the coordinates of the point. Therefore, the point can be seen more clearly if the equation is written as:<\/p>\n<div class=\"examplesentence\">\\(y-(-3)=-\\frac{1}{2}(x-4)\\)<br \/>\n<span style=\"font-size: 90%;\">(Subtracting a negative value is the same as addition.)<\/span><\/div>\n<p>\n&nbsp;<br \/>\nNow, we can see that this line travels through the point, \\((4,-3)\\) and has a slope of \\(m=-\\frac{1}{2}\\).<\/p>\n<h4 style=\"margin-bottom: 0em; text-transform: uppercase;\"><span id=\"Example_3_2\" class=\"m-toc-anchor\"><\/span>Example #3<\/h4>\n<p>\nLet\u2019s look at one more example:<\/p>\n<div class=\"examplesentence\">\\(y+12= -3(x+5)\\)<\/div>\n<p>\n&nbsp;<br \/>\nBy now, you can quickly see that the slope of this equation is \\(m=-3\\). This equation also does not \u201cmatch\u201d the general form but it can be rewritten as follows: \\(y-(-12)=-3(x-(-5))\\). This adjustment reveals that the point that is on the line, \\((-5,-12)\\).<\/p>\n<p>Once you feel comfortable with identifying the slope and the point from this form, you can graph the line as we did before.<\/p>\n<div class=\"examplesentence\">\\(y-5=\\frac{1}{2}(x-2)\\)<\/div>\n<p>\n&nbsp;<br \/>\n<strong>Step 1<\/strong>:  Identify the slope, \\(m=\\frac{1}{2}\\).<\/p>\n<p><strong>Step 2<\/strong>: Identify the point on the line, \\((2,5)\\).<\/p>\n<p>Some students find it helpful to \u201cswitch the sign\u201d of the given formula to determine the coordinates of the point!<\/p>\n<p><strong>Step 3<\/strong>: Plot the point, \\((2,5)\\), as the first point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65113\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9.png\" alt=\"plot the first point\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-9-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 4<\/strong>: <strong>M<\/strong>ove by \\(m=\\frac{1}{2}\\).<br \/>\nRise equals UP, 1<br \/>\nRun equals RIGHT, 2<br \/>\nPlot the 2nd point at \\((4,6)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65114\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10.png\" alt=\"move by m=1\/2\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-10-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 5<\/strong>: Repeat.<br \/>\nRise equals UP, 1<br \/>\nRun equals RIGHT, 2<br \/>\nPlot the 3rd point at \\((6,7)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65117\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1.png\" alt=\"repeat move by m=1\/2\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-11-1-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p><strong>Step 6<\/strong>: Draw a straight line through the three points. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65119\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1.png\" alt=\"draw a straight line through the points\" width=\"777\" height=\"437\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/image-12-1-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<hr>\n<p>\nAlright, we\u2019ve covered a lot of ground in this video regarding the different ways linear equations can be written. While the structure of the equations looks different, they all represent a line. The use of each depends on what you are given or what you are asked to do.<\/p>\n<p>That\u2019s all for this review! 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;\">What is slope-intercept form?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Slope-intercept form is \\(y = mx + b\\), where \\(m\\) is the slope and \\(b\\) is the \\(y\\)-intercept.<\/p>\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 slope-intercept form?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Graph slope-intercept form by first plotting the \\(y\\)-intercept, then using the slope to find a second point and plotting that point, and finally drawing a line through the two points.<\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 75%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Graph \\(y = 2x &#8211; 3\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">Plot the \\(y\\)-intercept: \\((0,-3)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-63169\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-1.png\" alt=\"\" width=\"272\" height=\"250\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-1.png 878w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-1-300x275.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-1-768x705.png 768w\" sizes=\"auto, (max-width: 272px) 100vw, 272px\" \/><\/p>\n<p>Find a second point using the slope.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-63168\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-2.png\" alt=\"\" width=\"284\" height=\"249\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-2.png 971w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-2-300x263.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-2-768x673.png 768w\" sizes=\"auto, (max-width: 284px) 100vw, 284px\" \/><\/p>\n<p>Draw a line through the two points<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-63165\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-3.png\" alt=\"\" width=\"256\" height=\"251\" style=\"margin-bottom: -0.75em\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-3.png 878w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-3-300x294.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2020\/12\/FAQ-Slope-Intercept-and-Point-Slope-Forms-2-3-768x753.png 768w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/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;\">What is \\(b\\) in slope-intercept form?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>In slope-intercept form, \\(b\\) stands for the \\(y\\)-intercept of the line.<\/p>\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;\">What is point-slope form?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Point-slope form is a linear equation in the form \\(y-y_1=m(x-x_1)\\).<\/p>\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 point-slope form?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>To graph point-slope form, first plot the point \\((x_1,y_1)\\). Then, use the slope (\\(m\\)) to find a second point on the line. Finally, draw a straight line through the two points.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\"> Graph \\(y-7=-4(x-1)\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">First, plot the point \\((x_1,y_1)\\), which in this case is \\((1,7)\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Graphing-example-02.svg\" alt=\"\" width=\"270\" height=\"270\" class=\"aligncenter size-full wp-image-229255\"  role=\"img\" \/><\/p>\n<p>Then, use the slope to find a second point. The slope is -4, so move right 1 and down 4. The new point is \\((2,3)\\). Plot this point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Graphing-example-03.svg\" alt=\"\" width=\"270\" height=\"270\" class=\"aligncenter size-full wp-image-229258\"  role=\"img\" \/><\/p>\n<p>Finally, draw a line through these two points.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Graphing-example-01.svg\" alt=\"\" width=\"270\" height=\"270\" class=\"aligncenter size-full wp-image-229252\"  role=\"img\" \/><\/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=\"SlopeIntercept_and_PointSlope_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Slope-Intercept and Point-Slope 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 \/>\nWhich of the following equations is 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=8(x+12)\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(3x+7y=19\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(y=4x-3\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(y-7=4(x-17)\\)<\/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 correct answer is \\(y=4x-3\\). Equations in slope-intercept are in the form \\(y=mx+b\\), where \\(m\\) is the slope and \\(b\\) is the \\(y\\)-intercept.<\/p>\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 of the following equations is in point-slope form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(7x+2=19y\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(y=3x+5\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(2x-9y=21\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">\\(y-11=2(x+14)\\)<\/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>The correct answer is \\(y-11=2(x+14)\\). Equations in point-slope form have the form \\(y-y_1=m(x-x_1)\\), where \\((x_1,y_1)\\) is a point on the line and \\(m\\) is the slope of the line.<\/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 of the following equations is in standard form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">\\(19x+3y=27\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(y-4=7(x+3)\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(y=2x+14\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(y-11=2(x-11)\\)<\/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 correct answer is \\(19x+3y=27\\). Equations in standard form have the form \\(Ax+By=C\\).<\/p>\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 the equation \\(3x+4y=12\\) in slope-intercept form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(y-12=3(x+4)\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(y-3=4(x+12)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">\\(y=-\\frac{3}{4}x+3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(y=-3x+8\\)<\/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>Equations in slope-intercept form have the form \\(y=mx+b\\). To get \\(3x+4y=12\\) in that form, manipulate the equation to isolate \\(y\\).<\/p>\n<p style=\"text-align:center;\">\\(3x+4y=12\\)<\/p>\n<p>Subtract \\(3x\\) from both sides.<\/p>\n<p style=\"text-align:center;\">\\(4y=12-3x\\)<\/p>\n<p>Divide both sides by 4.<\/p>\n<p style=\"text-align:center;\">\\(y=3-\\dfrac{3}{4}x\\)<\/p>\n<p>Rearrange the right side so it is in the proper form.<\/p>\n<p style=\"text-align:center;\">\\(y=-\\dfrac{3}{4}x+3\\)<\/p>\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 the point-slope equation \\(y-7=13(x+3)\\) in slope-intercept form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(3x-7y=13\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(7x+3y=13\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(y=7x-13\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">\\(y=13x+46\\)<\/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>Equations in slope-intercept form have the form \\(y=mx+b\\). To get \\(y-7=13(x+3)\\) in that form, manipulate the equation to isolate \\(y\\).<\/p>\n<p style=\"text-align:center;\">\\(y-7=13(x+3)\\)<\/p>\n<p>Distribute 13 to \\((x+3)\\).<\/p>\n<p style=\"text-align:center;\">\\(y-7=13x+39\\)<\/p>\n<p>Add 7 to both sides.<\/p>\n<p style=\"text-align:center;\">\\(y=13x+46\\)<\/p>\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":99721,"parent":0,"menu_order":34,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-684","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-linear-equations-videos","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/684","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=684"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/684\/revisions"}],"predecessor-version":[{"id":280331,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/684\/revisions\/280331"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99721"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}