{"id":26203,"date":"2025-06-19T11:02:28","date_gmt":"2025-06-19T11:02:28","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26203"},"modified":"2025-06-19T11:02:37","modified_gmt":"2025-06-19T11:02:37","slug":"write-the-equation-of-the-line-represented-by-y-2-3x-5-in-standard-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-equation-of-the-line-represented-by-y-2-3x-5-in-standard-form\/","title":{"rendered":"write the equation of the line represented by y = 2\/3x &#8211; 5 in standard form"},"content":{"rendered":"\n<p>write the equation of the line represented by y = 2\/3x &#8211; 5 in standard form.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The equation of the line y=23x\u22125y = \\frac{2}{3}x &#8211; 5 in <strong>standard form<\/strong> is: 2x\u22123y=152x &#8211; 3y = 15<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words):<\/strong><\/h3>\n\n\n\n<p>To convert a linear equation from <strong>slope-intercept form<\/strong> to <strong>standard form<\/strong>, we need to understand both formats:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Slope-intercept form<\/strong>: y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.<\/li>\n\n\n\n<li><strong>Standard form<\/strong>: Ax+By=CAx + By = C, where AA, BB, and CC are integers, and typically AA is positive.<\/li>\n<\/ul>\n\n\n\n<p>We start with the given equation: y=23x\u22125y = \\frac{2}{3}x &#8211; 5<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Eliminate the fraction<\/h4>\n\n\n\n<p>Multiply every term by the denominator (3) to eliminate the fraction: 3y=2x\u2212153y = 2x &#8211; 15<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Rearrange to standard form Ax+By=CAx + By = C<\/h4>\n\n\n\n<p>We want the xx and yy terms on the left side and the constant on the right: \u22122x+3y=\u221215-2x + 3y = -15<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Make AA positive<\/h4>\n\n\n\n<p>Standard form usually requires AA (the coefficient of xx) to be a <strong>positive<\/strong> integer. So, multiply the entire equation by -1: 2x\u22123y=152x &#8211; 3y = 15<\/p>\n\n\n\n<p>Now we have the equation in standard form.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why this matters:<\/h3>\n\n\n\n<p>Standard form is useful in algebra for solving systems of equations (e.g., using elimination or substitution), and in applications like graphing lines or finding intercepts quickly. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xx-intercept: Set y=0y = 0 \u2192 2x=152x = 15 \u2192 x=7.5x = 7.5<\/li>\n\n\n\n<li>yy-intercept: Set x=0x = 0 \u2192 \u22123y=15-3y = 15 \u2192 y=\u22125y = -5<\/li>\n<\/ul>\n\n\n\n<p>Thus, rewriting equations in standard form gives us flexibility in both algebraic operations and real-world applications.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>write the equation of the line represented by y = 2\/3x &#8211; 5 in standard form. The correct answer and explanation is: Correct Answer:The equation of the line y=23x\u22125y = \\frac{2}{3}x &#8211; 5 in standard form is: 2x\u22123y=152x &#8211; 3y = 15 Explanation (300 words): To convert a linear equation from slope-intercept form to standard [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26203","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26203"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26203\/revisions"}],"predecessor-version":[{"id":26205,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26203\/revisions\/26205"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}