To solve the linear equation \u22128x\u22125y=30-8x – 5y = 30\u22128x\u22125y=30, we can follow these steps:<\/p>\n\n\n\n
Step 1: Rearrange the equation to solve for yyy<\/h3>\n\n\n\n
Let’s start by isolating yyy in the equation. First, we need to get rid of the \u22128x-8x\u22128x term on the left-hand side. To do this, we can add 8x8x8x to both sides:\u22128x\u22125y+8x=30+8x-8x – 5y + 8x = 30 + 8x\u22128x\u22125y+8x=30+8x\u22125y=8x+30-5y = 8x + 30\u22125y=8x+30<\/p>\n\n\n\n
Step 2: Solve for yyy<\/h3>\n\n\n\n
Now, to solve for yyy, we need to divide both sides of the equation by \u22125-5\u22125:y=8x+30\u22125y = \\frac{8x + 30}{-5}y=\u221258x+30\u200b<\/p>\n\n\n\n
Step 3: Simplify the expression<\/h3>\n\n\n\n
Next, simplify the right-hand side. We can distribute the \u22125-5\u22125 into the terms in the numerator:y=8x\u22125+30\u22125y = \\frac{8x}{-5} + \\frac{30}{-5}y=\u221258x\u200b+\u2212530\u200by=\u22128×5\u22126y = -\\frac{8x}{5} – 6y=\u221258x\u200b\u22126<\/p>\n\n\n\n
Thus, the equation in slope-intercept form is:y=\u221285x\u22126y = -\\frac{8}{5}x – 6y=\u221258\u200bx\u22126<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The equation \u22128x\u22125y=30-8x – 5y = 30\u22128x\u22125y=30 is a linear equation, and it can be rewritten in slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.<\/p>\n\n\n\n
From the final equation y=\u221285x\u22126y = -\\frac{8}{5}x – 6y=\u221258\u200bx\u22126, we can observe that:<\/p>\n\n\n\n
- \n
- The slope mmm is \u221285-\\frac{8}{5}\u221258\u200b. This means that for every 5 units you move to the right along the x-axis, the value of yyy will decrease by 8 units.<\/li>\n\n\n\n
- The y-intercept bbb is \u22126-6\u22126, which means the line crosses the y-axis at the point (0,\u22126)(0, -6)(0,\u22126).<\/li>\n<\/ul>\n\n\n\n
This equation gives us a straight line where the relationship between xxx and yyy is linear, and you can graph it by plotting the y-intercept and using the slope to find other points.<\/p>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"-8x – 5y =30 The Correct Answer and Explanation is: To solve the linear equation \u22128x\u22125y=30-8x – 5y = 30\u22128x\u22125y=30, we can follow these steps: Step 1: Rearrange the equation to solve for yyy Let’s start by isolating yyy in the equation. First, we need to get rid of the \u22128x-8x\u22128x term on the left-hand […]<\/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-264068","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264068","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=264068"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264068\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}