To rewrite the equation 3x\u22128y=243x – 8y = 243x\u22128y=24 in slope-intercept form, we aim to solve for yyy and express the equation in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.<\/p>\n\n\n\n
Step 1: Isolate the yyy-term<\/h3>\n\n\n\n
We start with the equation:3x\u22128y=243x – 8y = 243x\u22128y=24<\/p>\n\n\n\n
The goal is to isolate yyy, so first subtract 3x3x3x from both sides:\u22128y=\u22123x+24-8y = -3x + 24\u22128y=\u22123x+24<\/p>\n\n\n\n
Step 2: Solve for yyy<\/h3>\n\n\n\n
Now, divide both sides of the equation by \u22128-8\u22128 to solve for yyy:y=\u22123x+24\u22128y = \\frac{-3x + 24}{-8}y=\u22128\u22123x+24\u200b<\/p>\n\n\n\n
Step 3: Simplify the equation<\/h3>\n\n\n\n
We can simplify each term in the numerator by dividing by \u22128-8\u22128:y=\u22123x\u22128+24\u22128y = \\frac{-3x}{-8} + \\frac{24}{-8}y=\u22128\u22123x\u200b+\u2212824\u200b<\/p>\n\n\n\n
This simplifies to:y=38x\u22123y = \\frac{3}{8}x – 3y=83\u200bx\u22123<\/p>\n\n\n\n
Step 4: Final result<\/h3>\n\n\n\n
Thus, the equation in slope-intercept form is:y=38x\u22123y = \\frac{3}{8}x – 3y=83\u200bx\u22123<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
In slope-intercept form, y=mx+by = mx + by=mx+b, the term mmm represents the slope of the line, and bbb represents the y-intercept, where the line crosses the y-axis. From our final equation:<\/p>\n\n\n\n
- \n
- The slope m=38m = \\frac{3}{8}m=83\u200b, meaning that for every 8 units the line moves horizontally (along the x-axis), it moves 3 units vertically (along the y-axis).<\/li>\n\n\n\n
- The y-intercept b=\u22123b = -3b=\u22123, which means the line crosses the y-axis at (0,\u22123)(0, -3)(0,\u22123).<\/li>\n<\/ul>\n\n\n\n
This form is useful because it makes it easy to graph the line or identify key features like the slope and y-intercept.<\/p>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"Rewrite the standard equation in slope-intercept form: 3x – 8y = 24 The Correct Answer and Explanation is: To rewrite the equation 3x\u22128y=243x – 8y = 243x\u22128y=24 in slope-intercept form, we aim to solve for yyy and express the equation in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb […]<\/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-246192","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246192","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=246192"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246192\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}