{"id":117349,"date":"2022-03-08T08:57:57","date_gmt":"2022-03-08T14:57:57","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=117349"},"modified":"2026-03-28T11:50:43","modified_gmt":"2026-03-28T16:50:43","slug":"finding-the-point-slope-form-equation","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/finding-the-point-slope-form-equation\/","title":{"rendered":"Finding the Point-Slope Form Equation"},"content":{"rendered":"<h1>Finding the Point-Slope Form Equation<\/h1>\n\n\t\t\t<div id=\"mmDeferVideoEncompass_an_XzcVyRG0\" 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_an_XzcVyRG0\" data-source-videoID=\"an_XzcVyRG0\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Finding the Point-Slope Form Equation Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Finding the Point-Slope Form Equation\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_an_XzcVyRG0:hover {cursor:pointer;} img#videoThumbnailImage_an_XzcVyRG0 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2330-thumbnail-1-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_an_XzcVyRG0\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_an_XzcVyRG0\" 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\",\"Finding the Point-Slope Form Equation\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_an_XzcVyRG0\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_an_XzcVyRG0\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_an_XzcVyRG0\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Today we\u2019re going to take a look at how to write an equation for a line in <strong>point-slope form<\/strong> when we are given a point on a line and its slope, and when we are given two points on the line. Remember, <a href=\"https:\/\/www.mometrix.com\/academy\/slope-intercept-and-point-slope-forms\/\"><strong>point-slope form<\/strong><\/a> is:<\/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-y_{1}=m(x-x_{1})\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>where \\((x_{1},y_{1})\\) is a point on the line, and \\(m\\) is the slope of the line.<\/p>\n<p>So, let&#8217;s start by finding the equation of the line that passes through the point \\((2,4)\\) and has a slope of 7.<\/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;\">Point: \\((2,4)\\) \tSlope: \\(7\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>When we are given these two things, all we have to do is plug in the values where they belong. First, let\u2019s write out our formula again:<\/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-y_{1}=m(x-x_{1})\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then we\u2019re going to write out the values that we\u2019re given:<\/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;\">\\(x_{1}=2\\)<br \/>\n&nbsp;<br \/>\n\\(y_{1}=4\\)<br \/>\n&nbsp;<br \/>\n\\(m=7\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>So, if we plug in our values into this equation, we&#8217;ll get:<\/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-4=7(x-2)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>So, our equation for this line is \\(y-4=7(x-2)\\). Let\u2019s try another one! <\/p>\n<p>Find the point-slope form equation for a line that passes through the point \\((-6,3)\\) and has a slope of 2.<\/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;\">Point: \\((-6,3)\\)\t\tSlope: \\(2\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>First, write out the values you are given.<\/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;\">\\(x_{1}=-6\\)<br \/>\n&nbsp;<br \/>\n\\(y_{1}=3\\)<br \/>\n&nbsp;<br \/>\n\\(m=2\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then we&#8217;re going to write out our formula, this will help us remember and make sure that we plug our values into the correct place.<\/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-y_{1}=m(x-x_{1})\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now, plug in the values you are given.<\/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-3=2(x-(-6))\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Finally, simplify the subtracting a negative part. Remember, when you subtract a negative number, it&#8217;s the same thing as adding that number, so we have:<\/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-3=2(x+6)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>And it\u2019s as simple as that!<\/p>\n<p>Now we&#8217;re going to take a look at how we find the point-slope form equation when we&#8217;re given two points on the line.<\/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;\">Points: \\((8,5)\\) and \\((-4,11)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Remember, when we&#8217;re given points on a line, that means that the line passes through these points. So, to write an equation in point-slope form, we need to know a point on the line and the slope of the line. We&#8217;re given two points to work with, but we don&#8217;t know the slope. To find the slope, we need to use the <a href=\"https:\/\/www.mometrix.com\/academy\/finding-the-slope-of-a-line\/\"><strong>slope formula<\/strong><\/a>.<\/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;\">\\(m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>For these points, let\u2019s call \\((8,5)\\) the point \\((x_{1},y_{1})\\) and \\((-4,11)\\) the point \\((x_{2},y_{2})\\). If you wanted to switch the points and have \\((-4,11)\\) be \\((x_{1},y_{1})\\) and \\((8,5)\\) be \\((x_{2},y_{2})\\), that\u2019s also perfectly acceptable. You\u2019ll get the right answer either way.<\/p>\n<p>Now, let\u2019s plug our values into the slope formula and solve for \\(m\\).<\/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;\">\\(m=\\frac{11-5}{-4-8}=\\frac{6}{-12}=-\\frac{1}{2}\\)\n<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now that we know our slope, let\u2019s choose one of the two points to write our formula. For this example, I\u2019m going to use the point \\((8,5)\\). You can absolutely use \\((-4,11)\\)  if you want to, and you will get a correct answer as well. It won&#8217;t be the exact same answer as using the point \\((8,5)\\), but if you follow the exact same steps, it will also be correct.<\/p>\n<p>Let\u2019s first list the values we are given.<\/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;\">\\(x_{1}=8\\)<br \/>\n&nbsp;<br \/>\n\\(y_{1}=5\\)<br \/>\n&nbsp;<br \/>\n\\(m=-\\frac{1}{2}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now, let\u2019s write our formula out.<\/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-y_{1}=m(x-x_{1})\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>And now we can plug in our values.<\/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-5=-\\frac{1}{2}(x-8)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>There\u2019s our answer! If you used the point \\((-4,11)\\) instead, your answer should be \\(y-11=-\\frac{1}{2}(x+4)\\). Either one of these two equations is correct.<\/p>\n<p>Let\u2019s try one more together before we go. Find the point-slope form equation for the line that passes through the points \\((6,-1)\\) and \\((8,7)\\).<\/p>\n<p>First, we need to find the slope of the line. Let\u2019s say the point \\((6,-1)\\) is \\((x_{1},y_{1})\\) and the point \\((8,7)\\) is \\((x_{2},y_{2})\\). First, write out the slope equation.<\/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;\">\\(m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now, plug in the values.<\/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;\">\\(m=\\frac{7-(-1)}{8-6}=\\frac{7+1}{8-6}=\\frac{8}{2}=\\frac{4}{1}=4\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now that we know the slope is 4, choose either one of the points to plug into the formula. For this example, let\u2019s use the point \\((6,-1)\\). First, we&#8217;re going to write out our known values.<\/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;\">\\(x_{1}=6\\)<br \/>\n&nbsp;<br \/>\n\\(y_{1}=-1\\)<br \/>\n&nbsp;<br \/>\n\\(m=4\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then we&#8217;re going to write out our formula.<\/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-y_{1}=m(x-x_{1})\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then we&#8217;re going to plug in our known values.<\/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-(-1)=4(x-6)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Finally, we&#8217;re going to simplify the left side, so we no longer have a subtracting a negative number. So, we&#8217;re going to make this:<\/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+1=4(x-6)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>If you chose the point \\((8,7)\\) instead, your answer should be \\(y-7=4(x-8)\\). Again, either one of these two formulas is an acceptable answer. So, \\(y-7=4(x-8)\\) and \\(y+1=4(x-6)\\) are both correct answers.<\/p>\n<p>I hope this video helped you get more comfortable with point-slope form. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<\/div>\n\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\"><strong>Return to Algebra I Videos<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finding the Point-Slope Form Equation &nbsp; Return to Algebra I Videos<\/p>\n","protected":false},"author":22,"featured_media":117352,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-117349","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"subject_matter-math"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"Want to know how to write an equation for a line in point-slope form? 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