{"id":116198,"date":"2022-03-02T13:44:15","date_gmt":"2022-03-02T19:44:15","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=116198"},"modified":"2026-03-28T11:50:06","modified_gmt":"2026-03-28T16:50:06","slug":"converting-between-standard-and-slope-intercept-forms","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/converting-between-standard-and-slope-intercept-forms\/","title":{"rendered":"Converting Between Standard and Slope-Intercept 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=\"Converting Between Standard and Slope-Intercept Forms Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Converting Between Standard and Slope-Intercept 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\/01\/2224-thumbnail-1-1-1.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\",\"Converting Between Standard and Slope-Intercept 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 AT4_Function() {\n  var x = document.getElementById(\"AT4\");\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=\"AT4_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=\"AT4\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Standard_and_SlopeIntercept_Form_Practice_Questions\" class=\"smooth-scroll\">Standard and Slope-Intercept Form 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=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Today we are going to take a look at how to convert linear equations between <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/slope-intercept-and-point-slope-forms\/\">standard form and slope-intercept form<\/a>. As a reminder, the <strong>standard form<\/strong> of a linear equation is:<\/p>\n<div class=\"examplesentence\">\\(Ax+By=C\\)<\/div>\n<p>\n&nbsp;<br \/>\nFor a standard form equation, \\(A\\) must be positive, and both \\(A\\) and \\(B\\) must be whole numbers. And the <strong>slope-intercept form<\/strong> of a linear equation is:<\/p>\n<div class=\"examplesentence\">\\(y=mx+b\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis is called slope-intercept form because the equation itself tells you the slope (\\(m\\)) and the \\(y\\)-intercept (\\(b\\)).<\/p>\n<p>So let\u2019s start with a simple example.<\/p>\n<h2><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h2>\n<p>\nConvert the standard form equation \\(x+y=2\\) to slope-intercept form.<\/p>\n<p>To convert from standard form to slope-intercept form, all we have to do is rearrange our equation to solve for \\(y\\) and then double check that our terms are in the correct order.<\/p>\n<p>So to do that with this equation, we have to subtract \\(x\\) from both sides.<\/p>\n<div class=\"examplesentence\">\\(x-x+y=2-x\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen we do that, our \\(x\\)&#8217;s cancel out and we&#8217;re left with:<\/p>\n<div class=\"examplesentence\">\\(y=2-x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, this is almost correct, but remember, slope-intercept form is \\(y=mx+b\\). That means that our \\(x\\)-term needs to be first. Because of the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/associative-property\/\">commutative property<\/a> of addition, we know that we can swap our two terms on the right side of our equation. So that will give us:<\/p>\n<div class=\"examplesentence\">\\(y=-x+2\\)<\/div>\n<p>\n&nbsp;<br \/>\nNotice that I kept the signs with each of the numbers, so we have minus \\(x\\) up here and that becomes \\(-x\\), and our 2 is positive up here and that becomes \\(+2\\). Making sure your signs are correct is super important when you do this. So now, because our equation is in slope-intercept form, we can easily see that our slope, \\(m\\), is equal to \\(-1\\), and our \\(y\\)-intercept, \\(b\\), is equal to 2.<\/p>\n<p>Let\u2019s try another one!<\/p>\n<h2><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h2>\n<p>\nConvert \\(2x-3y=6\\) to slope-intercept form.<\/p>\n<p>The first thing we need to do is solve our equation for \\(y\\). We can start by subtracting \\(2x\\) from both sides of our equation.<\/p>\n<div class=\"examplesentence\">\\(2x-2x-3y=6-2x\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo our \\(2x\\)&#8217;s cancel out over here, and we&#8217;re left with:<\/p>\n<div class=\"examplesentence\">\\(-3y=6-2x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, we divide both sides by \\(-3\\).<\/p>\n<div class=\"examplesentence\">\\(\\frac{-3y}{-3}=\\frac{6-2x}{-3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe need to divide the entire right side by \\(-3\\), so this means that each term needs to be divided by \\(-3\\). It\u2019s easy to want to only divide 6 by \\(-3\\), but this will give you an incorrect answer. So make sure you also divide \\(-2x\\) by \\(-3\\). So over here on our left side, our \\(-3\\)&#8217;s cancel out and we&#8217;re left with \\(y\\) equals, \\(6\\div (-3)=-2\\), because a positive divided by a negative is a negative. And then \\(-2x\\div (-3)=\\frac{2}{3}x\\), because a negative divided by a negative is equal to a positive.<\/p>\n<div class=\"examplesentence\">\\(y=-2+\\frac{2}{3}x\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo we almost have our correct answer, but we need to switch our terms on the right side. So that will give us:<\/p>\n<div class=\"examplesentence\">\\(y=\\frac{2}{3}x-2\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd we can see that our slope, \\(m\\), is equal to 23, and our \\(y\\)-intercept, \\(b\\), is equal to \\(-2\\).<\/p>\n<p>But what if we want to go the other way and convert a slope-intercept form equation to standard form? Let\u2019s take a look at an example!<\/p>\n<p>Convert \\(y=-4x+7\\) to standard form.<\/p>\n<p>Remember, standard form is \\(Ax+By=C\\). To convert to this form, all we have to do is bring our \\(x\\)-terms to the left side of the equation, then we\u2019ll make sure our \\(A\\)-value is positive and both our \\(A-\\) and \\(B-\\) values are whole numbers.<\/p>\n<p>So, to move this \\(x\\)-term to the left side of the equation, for this problem, we&#8217;re going to add \\(4x\\) to both sides.<\/p>\n<div class=\"examplesentence\">\\(y+4x=-4x+4x+7\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur \\(4x\\)&#8217;s will cancel out on the right side, and on the left side we&#8217;re left with:<\/p>\n<div class=\"examplesentence\">\\(y+4x=7\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we use the commutative property of addition to swap our terms on the left side and get:<\/p>\n<div class=\"examplesentence\">\\(4x+y=7\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, we check to make sure our \\(A\\)-value is positive and our \\(A-\\) and \\(B\\)-values are whole numbers. Both of these things are true, so this is our final answer.<\/p>\n<p>Let\u2019s try one more example.<\/p>\n<h2><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h2>\n<p>\nConvert \\(y=\\frac{4}{7} x-9\\) to standard form.<\/p>\n<p>For this equation, we&#8217;re going to start by multiplying the entire equation by 7 so that we can get rid of this fractional term..<\/p>\n<div class=\"examplesentence\">\\(7(y=\\frac{4}{7}x-9)\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo, \\(7\\cdot y=7y\\). \\(7\\cdot \\frac{4}{7}x\\), our 7&#8217;s will cancel out and that&#8217;ll leave us with \\(4x\\). And \\(7\\cdot 7(-9)=-63\\).<\/p>\n<div class=\"examplesentence\">\\(7y=4x-63\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo again, we&#8217;re going to bring our \\(x\\)-terms to the left side of the equation by subtracting \\(4x\\) from both sides.<\/p>\n<div class=\"examplesentence\">\\(7y-4x=4x-4x-63\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo that gives us:<\/p>\n<div class=\"examplesentence\">\\(7y-4x=-63\\)<\/div>\n<p>\n&nbsp;<\/p>\n<p>Now we&#8217;re going to swap our terms on the left side using the commutative property of addition to get:<\/p>\n<div class=\"examplesentence\">\\(-4x+7y=-63\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, we make sure that \\(A\\) is positive and both \\(A\\) and \\(B\\) are whole numbers. \\(A\\) is negative, so we need to deal with this first. To get rid of the negative in front of \\(A\\), we multiply the entire equation by \\(-1\\).<\/p>\n<div class=\"examplesentence\">\\(-1(-4x+7y=-63)\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhen we do this, we&#8217;ll get, \\(-1\\cdot (-4x)=-4x, -1\\cdot 7y=-7y\\), and \\(-1\\cdot (-63)=63\\).<\/p>\n<div class=\"examplesentence\">\\(4x-7y=63\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, our \\(A\\)-value is positive, and both \\(A-\\) and \\(B\\)-values are whole numbers, so this is our final answer.<\/p>\n<p>I hope this video helped you better understand how to convert between standard form and slope-intercept form of linear equations. Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Standard_and_SlopeIntercept_Form_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Standard and Slope-Intercept Form 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 \/>\nConvert the equation of the line \\(y=-4x+\\frac{3}{2}\\) to standard form.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(8x-2y=-3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\(8x+2y=3\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(4x+2y=6\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(4x-2y=-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 equation of a line in standard form is:<\/p>\n<p style=\"text-align: center;\">\\(Ax+By=C\\)<\/p>\n<ul>\n<li>\\(A\\), \\(B\\), and \\(C\\) are integers.<\/li>\n<li>\\(A>0\\)<\/li>\n<li>\\(A\\) and \\(B\\) cannot both be zero.<\/li>\n<\/ul>\n<p>First, let\u2019s clear out the fraction for the equation of our line that is in slope-intercept form by multiplying both sides of the equation by the denominator of the fraction. In this case, multiply both sides of the equation by 2.<\/p>\n<p style=\"text-align: center;\">\\(2\\cdot y=2(-4x+\\frac{3}{2})\\)<\/p>\n<p style=\"text-align: center;\">\\(2y=2(-4x)+2\\cdot \\frac{3}{2}\\)<\/p>\n<p style=\"text-align: center;\">\\(2y=-8x+3\\)<\/p>\n<p>Now, move the x-term to the left-hand side of the equation by subtracting \\(8x\\) from both sides.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(2y+8x=-8x+3+8x\\)<br \/>\n\\(8x+2y=3\\)<\/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 \/>\nConvert the equation of the line \\(2x-7y=14\\) to slope-intercept form.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(y=\\frac{2}{7}x-2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(y=-\\frac{2}{7}x+2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(y=\\frac{7}{2}x-14\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(y=-\\frac{7}{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 given equation is in standard form. The equation of a line in slope-intercept form is:<\/p>\n<p style=\"text-align: center;\">\\(y=mx+b\\)<\/p>\n<ul>\n<li>\\(m\\) is the slope of the line.<\/li>\n<li>\\(b\\) is the \\(y\\)-intercept of the line.<\/li>\n<\/ul>\n<p>To convert the equation of our line to slope-intercept form, we need to isolate the \\(y\\)-value. Start by subtracting \\(2x\\) from both sides.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(2x-7y-2x=14-2x\\)<br \/>\n\\(-7y=14-2x\\)<\/p>\n<p>Next, divide both sides by \u22127.<\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(\\large{\\frac{-7y}{-7}}\\normalsize{=}\\large{\\frac{14-2x}{-7}}\\)<br \/>\n\\(y=-2+\\large{\\frac{2}{7}}\\normalsize{x}\\)<\/p>\n<p>Rearranging the terms on the right-hand side of the equation, we get:<\/p>\n<p style=\"text-align: center;\">\\(y=\\large{\\frac{2}{7}}\\normalsize{x-2}\\)<\/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 \/>\nConvert the equation of the line \\(y=\\frac{3}{5}x-2\\) to standard form.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(3x-5y=-2\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(5x+3y=2\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\(3x-5y=10\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(3x-5y=-10\\)<\/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 given equation is in slope-intercept form. The equation of a line in standard form is:<\/p>\n<p style=\"text-align: center;\">\\(Ax+By=C\\)<\/p>\n<ul>\n<li>\\(A\\), \\(B\\), and \\(C\\) are integers.<\/li>\n<li>\\(A>0\\)<\/li>\n<li>\\(A\\) and \\(B\\) cannot both be zero.<\/li>\n<\/ul>\n<p>First, let\u2019s clear out the fraction for the equation of our line by multiplying both sides of the equation by the denominator of the fraction. In this case, multiply both sides of the equation by 5.<\/p>\n<p style=\"text-align: center;\">\\(5\\cdot y=5(\\frac{3}{5}x-2)\\)<\/p>\n<p style=\"text-align: center;\">\\(5y=5\\cdot\\frac{3}{5}x-5\\cdot2\\)<\/p>\n<p style=\"text-align: center;\">\\(5y=3x-10\\)<\/p>\n<p>Next, we need to be sure the terms containing \\(x\\) and \\(y\\) are on the left-hand side of the equation. To do so, subtract \\(3x\\) from both sides.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(5y-3x=3x-10-3x\\)<br \/>\n\\(-3x+5y=-10\\)<\/p>\n<p>In the standard form equation of a line, A must be greater than zero. So, multiply both sides of the equation by \u22121. <\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(-1(-3x+5y)=-1\\cdot-10\\)<br \/>\n\\(3x-5y=10\\)<\/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 \/>\nYou want to join a fitness program. To become a member, there is an initial fee of $75 and a monthly fee of $25. The equation for the total cost can be modeled by the equation \\(y=25x+75\\), where \\(x\\) represents the number of months of membership, and \\(y\\) represents the total cost, in dollars, of being a member. Which of the following is the equation of the total cost of membership in standard form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(75-y=-25x\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(75+y=25x\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">\\(25x-y=-75\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(25x+y=75\\)<\/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>The equation of a line in standard form is:<\/p>\n<p style=\"text-align: center;\">\\(Ax+By=C\\)<\/p>\n<ul>\n<li>\\(A\\), \\(B\\), and \\(C\\) are integers.<\/li>\n<li>\\(A>0\\)<\/li>\n<li>\\(A\\) and \\(B\\) cannot both be zero.<\/li>\n<\/ul>\n<p>First, we need to be sure the terms containing \\(x\\) and \\(y\\) are on the left-hand side of the equation. So, subtract \\(25x\\) from both sides of the equation.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(y-25x=25x+75-25x\\)<br \/>\n\\(-25x+y=75\\)<\/p>\n<p>In the standard form of a line, \\(A\\) must be greater than zero. So, multiply both sides of the equation by -1. <\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(-1(-25x+y)=-1\\cdot75\\)<br \/>\n\\(25x-y=-75\\)<\/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 \/>\nYou want to produce 10 ounces of an acid solution that is 25% acid. To produce the solution, you mix a 20% acid solution with a 30% acid solution. The equation \\(\\frac{1}{5}x+\\frac{3}{10}y=10\\) can be used to represent the number of ounces of the two solutions that are mixed to make the 25% acid solution where \\(x\\) is the number of ounces of the 20% acid solution and \\(y\\) is the number of ounces of the 30% acid solution. Which of the following is the equation of the two solutions that are mixed to make the 25% acid solution in slope-intercept form?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">\\(y=-\\frac{2}{3}x+\\frac{100}{3}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(y=\\frac{2}{3}x-\\frac{100}{3}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(y=-\\frac{2}{3}x+100\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(y=\\frac{2}{3}x-100\\)<\/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>The equation of a line in slope-intercept form is:<\/p>\n<p style=\"text-align: center;\">\\(y=mx+b\\)<\/p>\n<ul>\n<li>\\(m\\) is the slope of the line.<\/li>\n<li>\\(b\\) is the \\(y\\)-intercept of the line.<\/li>\n<\/ul>\n<p>First, let\u2019s clear out the fraction for the equation of our line by multiplying both sides of the equation by the least common multiple of the two denominators. The least common multiple of 5 and 10 is 10, so multiply both sides of the equation by 10.<\/p>\n<p style=\"text-align: center;\">\\(10(\\frac{1}{5}x+\\frac{3}{10}y)=10\\cdot10\\)<\/p>\n<p style=\"text-align: center;\">\\(10\\cdot\\frac{1}{5}x+10\\cdot\\frac{3}{10}y=100\\)<\/p>\n<p style=\"text-align: center;\">\\(2x+3y=100\\)<\/p>\n<p>To convert the equation from standard form to slope-intercept form, we need to isolate the \\(y\\)-value. Start by subtracting \\(2x\\) from both sides.<\/p>\n<p style=\"text-align: center; line-height: 40px\">\\(2x+3y-2x=100-2x\\)<br \/>\n\\(3y=100-2x\\)<\/p>\n<p>Then, divide both sides of the equation by 3.<\/p>\n<p style=\"text-align: center;\">\\(\\large{\\frac{3y}{3}}\\normalsize{=}\\large{\\frac{100-2x}{3}}\\)<\/p>\n<p>Rearranging the terms on the right-hand side of the equation, we get:<\/p>\n<p style=\"text-align: center;\">\\(y=-\\frac{2}{3}x+\\frac{100}{3}\\)<\/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":22,"featured_media":116201,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-116198","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116198","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=116198"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116198\/revisions"}],"predecessor-version":[{"id":281135,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/116198\/revisions\/281135"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/116201"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=116198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}