{"id":170646,"date":"2024-11-19T22:01:40","date_gmt":"2024-11-19T22:01:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170646"},"modified":"2024-11-19T22:01:41","modified_gmt":"2024-11-19T22:01:41","slug":"which-equations-are-in-standard-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/which-equations-are-in-standard-form\/","title":{"rendered":"Which equations are in standard form"},"content":{"rendered":"\n<p>Which equations are in standard form? Check all that apply y = 2x + 5 2x + 3y = \u20136 \u20134x + 3y = 12 y = y equals StartFraction 3 Over 2 EndFraction x minus 9.x \u2013 9 StartFraction one-half EndFraction x plus 3 equals 6.x + 3 = 6 x \u2013 y = 5 5x + 3y = 5 x plus 3 y equals StartFraction one-half EndFraction.<\/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 equations are in <strong>standard form<\/strong>, we need to recognize the general form of the equation of a line in two variables, which is:<\/p>\n\n\n\n<p>[<br>Ax + By = C<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A ) and ( B ) are <strong>integers<\/strong> (with ( A ) being nonzero),<\/li>\n\n\n\n<li>( x ) and ( y ) are variables,<\/li>\n\n\n\n<li>( C ) is a constant.<\/li>\n<\/ul>\n\n\n\n<p>The equation should have all variables on one side, and the coefficients of ( x ) and ( y ) should be integers.<\/p>\n\n\n\n<p>Let&#8217;s go through the equations one by one and check if they are in standard form:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>( y = 2x + 5 )<\/strong><br>This equation is <strong>not<\/strong> in standard form because it is written in slope-intercept form ( y = mx + b ). To put it in standard form, subtract ( 2x ) from both sides:<br>[<br>-2x + y = 5<br>]<br>This would be in standard form.<\/li>\n\n\n\n<li><strong>( 2x + 3y = -6 )<\/strong><br>This equation <strong>is<\/strong> in standard form. It has the format ( Ax + By = C ), with ( A = 2 ), ( B = 3 ), and ( C = -6 ).<\/li>\n\n\n\n<li><strong>( -4x + 3y = 12 )<\/strong><br>This equation <strong>is<\/strong> in standard form. It has ( A = -4 ), ( B = 3 ), and ( C = 12 ).<\/li>\n\n\n\n<li><strong>( y = \\frac{3}{2}x &#8211; 9 )<\/strong><br>This equation is in slope-intercept form. To put it into standard form, multiply through by 2 to eliminate the fraction:<br>[<br>2y = 3x &#8211; 18<br>]<br>Then, subtract ( 3x ) from both sides to get:<br>[<br>-3x + 2y = -18<br>]<br>Now, it is in standard form.<\/li>\n\n\n\n<li><strong>( \\frac{1}{2}x + 3 = 6 )<\/strong><br>This equation is <strong>not<\/strong> in standard form. First, subtract 3 from both sides:<br>[<br>\\frac{1}{2}x = 3<br>]<br>Then multiply through by 2 to eliminate the fraction:<br>[<br>x = 6<br>]<br>This is not in standard form.<\/li>\n\n\n\n<li><strong>( x &#8211; y = 5 )<\/strong><br>This equation <strong>is<\/strong> in standard form. It has ( A = 1 ), ( B = -1 ), and ( C = 5 ).<\/li>\n\n\n\n<li><strong>( 5x + 3y = 5 )<\/strong><br>This equation <strong>is<\/strong> in standard form. It is already in the correct form ( Ax + By = C ), with ( A = 5 ), ( B = 3 ), and ( C = 5 ).<\/li>\n\n\n\n<li><strong>( x + 3y = \\frac{1}{2} )<\/strong><br>This equation is <strong>not<\/strong> in standard form because of the fraction on the right side. To convert to standard form, multiply through by 2:<br>[<br>2x + 6y = 1<br>]<br>Now, it is in standard form.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of equations in standard form:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 2x + 3y = -6 )<\/li>\n\n\n\n<li>( -4x + 3y = 12 )<\/li>\n\n\n\n<li>( -3x + 2y = -18 ) (from the equation ( y = \\frac{3}{2}x &#8211; 9 ))<\/li>\n\n\n\n<li>( x &#8211; y = 5 )<\/li>\n\n\n\n<li>( 5x + 3y = 5 )<\/li>\n\n\n\n<li>( 2x + 6y = 1 ) (from the equation ( x + 3y = \\frac{1}{2} ))<\/li>\n<\/ul>\n\n\n\n<p>These are the equations that are in standard form.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which equations are in standard form? Check all that apply y = 2x + 5 2x + 3y = \u20136 \u20134x + 3y = 12 y = y equals StartFraction 3 Over 2 EndFraction x minus 9.x \u2013 9 StartFraction one-half EndFraction x plus 3 equals 6.x + 3 = 6 x \u2013 y = [&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-170646","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170646","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=170646"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170646\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}