{"id":220852,"date":"2025-05-28T20:49:24","date_gmt":"2025-05-28T20:49:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220852"},"modified":"2025-05-28T20:49:27","modified_gmt":"2025-05-28T20:49:27","slug":"write-the-linear-function-and-determine-the-slope-of-the-line","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/write-the-linear-function-and-determine-the-slope-of-the-line\/","title":{"rendered":"Write The Linear Function And Determine The Slope Of The Line"},"content":{"rendered":"\n

For The Line 6x + 3y = 24, Write The Linear Function And Determine The Slope Of The Line Y = 24 – 6X And The Slope Is + 24 Y = 8 – 2x And The Slope Is – 2 Y= 8 + 2X And The Slope Is + 2 Y = 8 – 2x And The Slope Is + 2<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the linear function and slope from the given equation:<\/p>\n\n\n\n

Given:<\/strong>
6x+3y=246x + 3y = 24<\/p>\n\n\n\n

Step 1: Solve for yy in terms of xx (i.e., convert to slope-intercept form: y=mx+by = mx + b)<\/h3>\n\n\n\n

Start with the original equation: 6x+3y=246x + 3y = 24<\/p>\n\n\n\n

Subtract 6x6x from both sides: 3y=\u22126x+243y = -6x + 24<\/p>\n\n\n\n

Divide all terms by 3: y=\u22122x+8y = -2x + 8<\/p>\n\n\n\n

This is the linear function in slope-intercept form, where:<\/p>\n\n\n\n

    \n
  • m=\u22122m = -2 (the coefficient of xx) is the slope<\/strong><\/li>\n\n\n\n
  • b=8b = 8 is the y-intercept<\/strong><\/li>\n<\/ul>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    y=\u22122x+8 and the slope is \u22122\\boxed{y = -2x + 8 \\text{ and the slope is } -2}<\/p>\n\n\n\n

    Explanation <\/h3>\n\n\n\n

    To find the slope of a line given in standard form, you must first rearrange the equation into the slope-intercept form, y=mx+by = mx + b, where mm represents the slope and bb represents the y-intercept.<\/p>\n\n\n\n

    The original equation is 6x+3y=246x + 3y = 24, which is in standard form Ax+By=CAx + By = C. To convert this into slope-intercept form, solve for yy:<\/p>\n\n\n\n

    Subtract 6x6x from both sides to isolate the yy-term: 3y=\u22126x+243y = -6x + 24<\/p>\n\n\n\n

    Next, divide every term by 3 to solve for yy: y=\u22122x+8y = -2x + 8<\/p>\n\n\n\n

    Now the equation is in the form y=mx+by = mx + b, where the slope m=\u22122m = -2. This slope tells us that for every unit increase in xx, yy decreases by 2 units, indicating a line that goes downward from left to right.<\/p>\n\n\n\n

    Among the answer choices, only one correctly matches the function and the slope:<\/p>\n\n\n\n

      \n
    • \u201cY = 8 – 2X and the slope is -2\u201d<\/strong> is correct.<\/li>\n<\/ul>\n\n\n\n

      The other options either miscalculate the slope or the expression for yy. For instance, \u201cY = 24 – 6X and the slope is +24\u201d is incorrect because the slope would be \u22126-6, not +24+24, and the equation doesn\u2019t match the rearranged form. Thus, understanding how to isolate yy and identify the slope is essential in linear algebra.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      For The Line 6x + 3y = 24, Write The Linear Function And Determine The Slope Of The Line Y = 24 – 6X And The Slope Is + 24 Y = 8 – 2x And The Slope Is – 2 Y= 8 + 2X And The Slope Is + 2 Y = 8 – […]<\/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-220852","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220852","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=220852"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220852\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}