{"id":146266,"date":"2024-09-30T14:33:17","date_gmt":"2024-09-30T14:33:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146266"},"modified":"2024-09-30T14:33:19","modified_gmt":"2024-09-30T14:33:19","slug":"what-is-an-equivalent-equation-solved-for-y2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/what-is-an-equivalent-equation-solved-for-y2\/","title":{"rendered":"What is an equivalent equation solved for y2"},"content":{"rendered":"\n<p>What is an equivalent equation solved for y2? y2 = mx2 \u2013 x1 y1 y2 = mx2 \u2013 x1 \u2013 y1 y2 = m(x2 \u2013 x1) y1 y2 = m(x2 \u2013 x1) \u2013 y1<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine which equation is equivalent to (y_2), let\u2019s start with the given options and analyze them step-by-step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Starting Equation<\/strong>: The original equation is (y_2 = mx_2 &#8211; x_1y_1).<\/li>\n\n\n\n<li><strong>Options<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(y_2 = mx_2 &#8211; x_1 &#8211; y_1)<\/li>\n\n\n\n<li>(y_2 = m(x_2 &#8211; x_1))<\/li>\n\n\n\n<li>(y_2 = m(x_2 &#8211; x_1) &#8211; y_1)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Evaluating Each Option:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>First Option: (y_2 = mx_2 &#8211; x_1 &#8211; y_1)<\/strong><br>This option is not equivalent to the original equation. The term (-y_1) is introduced without justification, making this equation distinct from the original.<\/li>\n\n\n\n<li><strong>Second Option: (y_2 = m(x_2 &#8211; x_1))<\/strong><br>This option rewrites (y_2) in a form based on the slope-intercept concept but removes any influence of (y_1) and (x_1) inappropriately. Thus, it does not hold equivalent value to the original equation.<\/li>\n\n\n\n<li><strong>Third Option: (y_2 = m(x_2 &#8211; x_1) &#8211; y_1)<\/strong><br>This equation can be rearranged to show its equivalence to the original. Start with (y_2 = m(x_2 &#8211; x_1) &#8211; y_1):<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Adding (y_1) to both sides gives:<br>[<br>y_2 + y_1 = m(x_2 &#8211; x_1)<br>]<\/li>\n\n\n\n<li>This shows a relationship involving both (y_2) and (y_1), which aligns with the concept of a slope in the coordinate system where (m) is the slope, and the differences in (x) values are accounted for.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>After evaluating the options, <strong>the equivalent equation solved for (y_2) is<\/strong>:<br>[ y_2 = m(x_2 &#8211; x_1) &#8211; y_1 ]<\/p>\n\n\n\n<p>This option correctly captures the relationship defined by the original equation while maintaining the role of (y_1). Understanding these transformations is crucial in algebra, particularly in linear equations where slope-intercept form often plays a significant role. By manipulating the equations, we can derive relationships and understand how different variables interact within a given context.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is an equivalent equation solved for y2? y2 = mx2 \u2013 x1 y1 y2 = mx2 \u2013 x1 \u2013 y1 y2 = m(x2 \u2013 x1) y1 y2 = m(x2 \u2013 x1) \u2013 y1 The Correct Answer and Explanation is : To determine which equation is equivalent to (y_2), let\u2019s start with the given options [&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-146266","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146266","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=146266"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146266\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}