{"id":233857,"date":"2025-06-13T13:16:23","date_gmt":"2025-06-13T13:16:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233857"},"modified":"2025-06-13T13:16:26","modified_gmt":"2025-06-13T13:16:26","slug":"1-2x-y-10-i-have-to-do-some-stupid-slope-intercept-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/1-2x-y-10-i-have-to-do-some-stupid-slope-intercept-form\/","title":{"rendered":"-1\/2x + y = 10. I have to do some stupid slope-intercept form."},"content":{"rendered":"\n<p>-1\/2x + y = 10. I have to do some stupid slope-intercept form.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To write the equation <strong>\u2013\u00bdx + y = 10<\/strong> in <strong>slope-intercept form<\/strong>, we need to rearrange it into the form:y=mx+by = mx + by=mx+b<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>m<\/strong> is the <strong>slope<\/strong> of the line, and<\/li>\n\n\n\n<li><strong>b<\/strong> is the <strong>y-intercept<\/strong> (the point where the line crosses the y-axis).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step-by-step Solution:<\/strong><\/h3>\n\n\n\n<p>We start with the equation:\u221212x+y=10- \\frac{1}{2}x + y = 10\u221221\u200bx+y=10<\/p>\n\n\n\n<p>To write this in slope-intercept form, isolate <strong>y<\/strong>:y=12x+10y = \\frac{1}{2}x + 10y=21\u200bx+10<\/p>\n\n\n\n<p>That\u2019s it! The equation is now in slope-intercept form:y=12x+10\\boxed{y = \\frac{1}{2}x + 10}y=21\u200bx+10\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (Like in the textbooks):<\/strong><\/h3>\n\n\n\n<p>The slope-intercept form of a linear equation is used to graph lines easily and understand how the variables relate to each other. The general formula is:y=mx+by = mx + by=mx+b<\/p>\n\n\n\n<p>Here, <strong>m<\/strong> represents the <strong>slope<\/strong>\u2014how steep the line is\u2014and <strong>b<\/strong> represents the <strong>y-intercept<\/strong>, the value of <strong>y<\/strong> when <strong>x = 0<\/strong>.<\/p>\n\n\n\n<p>In the equation <strong>\u2013\u00bdx + y = 10<\/strong>, the variable <strong>y<\/strong> is already by itself on one side, but the <strong>x<\/strong> term is not yet in the form we want. To solve this, we simply add <strong>\u00bdx<\/strong> to both sides of the equation to move it over. That gives:y=12x+10y = \\frac{1}{2}x + 10y=21\u200bx+10<\/p>\n\n\n\n<p>Now the equation is in the desired slope-intercept form. From this, we can directly identify:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>slope (m)<\/strong> is <strong>\u00bd<\/strong>, which means for every 2 units you move horizontally, the line rises by 1 unit.<\/li>\n\n\n\n<li>The <strong>y-intercept (b)<\/strong> is <strong>10<\/strong>, which means the line crosses the y-axis at (0, 10).<\/li>\n<\/ul>\n\n\n\n<p>This form is very useful in algebra for graphing and analyzing linear relationships.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-348.jpeg\" alt=\"\" class=\"wp-image-233858\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>-1\/2x + y = 10. I have to do some stupid slope-intercept form. The Correct Answer and Explanation is: To write the equation \u2013\u00bdx + y = 10 in slope-intercept form, we need to rearrange it into the form:y=mx+by = mx + by=mx+b where: Step-by-step Solution: We start with the equation:\u221212x+y=10- \\frac{1}{2}x + y = [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233857","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233857","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233857"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233857\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}