{"id":154840,"date":"2024-10-15T13:53:51","date_gmt":"2024-10-15T13:53:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=154840"},"modified":"2024-10-15T13:53:53","modified_gmt":"2024-10-15T13:53:53","slug":"write-y-2x-in-standard-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/15\/write-y-2x-in-standard-form\/","title":{"rendered":"Write y = -2x in standard form."},"content":{"rendered":"\n<p>Write y = -2x in standard form. Then graph the function.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To convert the equation ( y = -2x ) into standard form, we need to rearrange it into the form ( Ax + By = C ), where ( A ), ( B ), and ( C ) are integers, and ( A ) should be a non-negative integer.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Rearranging the Equation<\/h3>\n\n\n\n<p>Starting with the equation:<br>[<br>y = -2x<br>]<\/p>\n\n\n\n<p>We can add ( 2x ) to both sides to get:<br>[<br>2x + y = 0<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Standard Form<\/h3>\n\n\n\n<p>Now, we have the equation in standard form:<br>[<br>2x + y = 0<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Graphing the Function<\/h3>\n\n\n\n<p>To graph the equation ( y = -2x ) or ( 2x + y = 0 ), we can find two points by substituting values for ( x ) and solving for ( y ).<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding Points:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When ( x = 0 ):<br>[<br>y = -2(0) = 0 \\quad \\Rightarrow \\quad (0, 0)<br>]<\/li>\n\n\n\n<li>When ( x = 1 ):<br>[<br>y = -2(1) = -2 \\quad \\Rightarrow \\quad (1, -2)<br>]<\/li>\n\n\n\n<li>When ( x = -1 ):<br>[<br>y = -2(-1) = 2 \\quad \\Rightarrow \\quad (-1, 2)<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Plotting the Points:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plot the points ( (0, 0) ), ( (1, -2) ), and ( (-1, 2) ) on the Cartesian plane.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Drawing the Line:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Connect the points with a straight line. The line will slope downward, reflecting the negative coefficient of ( x ) in the equation.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Graph<\/h3>\n\n\n\n<p>The graph of the equation ( y = -2x ) depicts a straight line with a slope of (-2), which indicates that for every unit increase in ( x ), ( y ) decreases by 2 units. The line intersects the y-axis at the origin ((0, 0)), which is the y-intercept. Since the slope is negative, the line will move downwards from left to right, demonstrating the inverse relationship between ( x ) and ( y ) in this linear equation. The standard form ( 2x + y = 0 ) is useful in easily identifying the slope and intercepts of the line, making it applicable for various mathematical analyses and real-world applications.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write y = -2x in standard form. Then graph the function. The Correct Answer and Explanation is: To convert the equation ( y = -2x ) into standard form, we need to rearrange it into the form ( Ax + By = C ), where ( A ), ( B ), and ( C ) [&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-154840","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154840","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=154840"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154840\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}