{"id":39346,"date":"2025-06-27T06:51:17","date_gmt":"2025-06-27T06:51:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39346"},"modified":"2025-06-27T06:51:18","modified_gmt":"2025-06-27T06:51:18","slug":"is-5x-10y20-and-y-2x6-parallel-perpendicular-or-neither","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/is-5x-10y20-and-y-2x6-parallel-perpendicular-or-neither\/","title":{"rendered":"Is 5x-10y+20 and y=-2x+6 parallel perpendicular or neither"},"content":{"rendered":"\n<p>Is 5x-10y+20 and y=-2x+6 parallel perpendicular or neither<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine whether the lines represented by the equations 5x\u221210y+20=05x &#8211; 10y + 20 = 0 and y=\u22122x+6y = -2x + 6 are parallel, perpendicular, or neither, it is necessary to compare their slopes.<\/p>\n\n\n\n<p>First, rewrite the equation 5x\u221210y+20=05x &#8211; 10y + 20 = 0 in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope.<\/p>\n\n\n\n<p>Start by isolating yy: 5x\u221210y+20=05x &#8211; 10y + 20 = 0 \u221210y=\u22125x\u221220-10y = -5x &#8211; 20 y=\u22125x\u221220\u221210=5&#215;10+2010=12x+2y = \\frac{-5x &#8211; 20}{-10} = \\frac{5x}{10} + \\frac{20}{10} = \\frac{1}{2}x + 2<\/p>\n\n\n\n<p>The slope of the first line is 12\\frac{1}{2}.<\/p>\n\n\n\n<p>The second line is already in slope-intercept form: y=\u22122x+6y = -2x + 6<\/p>\n\n\n\n<p>The slope of the second line is \u22122-2.<\/p>\n\n\n\n<p>Next, analyze the relationship between these slopes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two lines are parallel if their slopes are equal.<\/li>\n\n\n\n<li>Two lines are perpendicular if the product of their slopes is \u22121-1.<\/li>\n\n\n\n<li>If neither condition is met, the lines are neither parallel nor perpendicular.<\/li>\n<\/ul>\n\n\n\n<p>Calculate the product of the slopes: (12)\u00d7(\u22122)=\u22121\\left(\\frac{1}{2}\\right) \\times (-2) = -1<\/p>\n\n\n\n<p>Since the product of the slopes is \u22121-1, the two lines are perpendicular.<\/p>\n\n\n\n<p><strong>Summary:<\/strong><\/p>\n\n\n\n<p>The first line has slope 12\\frac{1}{2}, and the second line has slope \u22122-2. The product of the slopes is \u22121-1, which means the lines are perpendicular. Lines with slopes that multiply to \u22121-1 always intersect at a right angle. Therefore, these two lines are perpendicular to each other.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is 5x-10y+20 and y=-2x+6 parallel perpendicular or neither The correct answer and explanation is: To determine whether the lines represented by the equations 5x\u221210y+20=05x &#8211; 10y + 20 = 0 and y=\u22122x+6y = -2x + 6 are parallel, perpendicular, or neither, it is necessary to compare their slopes. First, rewrite the equation 5x\u221210y+20=05x &#8211; 10y [&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-39346","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39346","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=39346"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39346\/revisions"}],"predecessor-version":[{"id":39347,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39346\/revisions\/39347"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39346"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39346"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}