{"id":9025,"date":"2016-07-04T02:33:10","date_gmt":"2016-07-04T02:33:10","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=9025"},"modified":"2016-07-04T02:33:10","modified_gmt":"2016-07-04T02:33:10","slug":"math-review-of-parallel-and-perpendicular-lines","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/07\/04\/math-review-of-parallel-and-perpendicular-lines\/","title":{"rendered":"Math Review of Parallel and Perpendicular Lines"},"content":{"rendered":"

Overview<\/h3>\n

Parallel lines never intersect when they are graphed on the same plane, while perpendicular lines are lines that intersect at one point at right angles to each other.\u00a0 Their linear equations have special relationships.<\/p>\n

Parallel Lines<\/h3>\n

Parallel lines are lines in the same plane that have no points in common.\u00a0 Suppose that one line has the equation y = 2x.\u00a0 In slope-intercept form, its slope would be 2 and the y-intercept would be 0.\u00a0 Suppose that another line in the same plane has the equation y = 2x +4.\u00a0 In that case, its slope is still 2 but the y-intercept is 4.\u00a0 Those lines would have no points in common, because there isn\u2019t any point that would be a solution of both equations.\u00a0 Therefore the lines would not intersect, and they are parallel.<\/p>\n

Solving Equations for Parallel Lines<\/h3>\n

In the example of y=2x and y=2x +4, both lines have the same slope, 2, and the y-intercepts are different.\u00a0 Both equations are already solved for y.\u00a0 Given pairs of equations, they can both be put in slope-intercept form and solved for y to determine the slope and the y-intercept. \u00a0If the slopes of the lines are equal and the y-intercepts are not the same, the lines are parallel.\u00a0 Suppose the equations for the lines are y = -3x +4 and 6x +2y = -10.\u00a0 Are those lines parallel?\u00a0 The slope of the line y = -3x +4 is already -3 and the y intercept is +4.\u00a0 Solving the second equation for y takes place in 2 steps, because 2y = -6x -10, moving the 6x, so y equals (-6\/2) x \u2013 (10\/2), or -3x -5.\u00a0 The slope of both lines is -3 but the y-intercepts are different, so they are parallel.<\/p>\n

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Perpendicular Lines<\/h3>\n

Perpendicular lines are lines that are in the same plane that intersect at one point, forming a 90\u00b0 angle (a right angle).\u00a0 Slopes that have a product of -1 are perpendicular. Suppose a line has the equation y = 2x -3 and another line has the equation y = ( -1\/2) x -4.\u00a0 The product of the slopes, 2(-1\/2) is -1, so they are perpendicular.<\/p>\n

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Solving\u00a0Equations for Perpendicular Lines<\/h3>\n

In order to determine of two equations are for perpendicular lines, solve for y and determine the product of the slopes.\u00a0 Suppose the equations are 3y = 9x +3 and 6y +2x =6 are perpendicular.\u00a0 Solving for y, 3y=9x +3 can be simplified to y = 3x +1 by dividing both sides by 3.\u00a0 Solving for y, 6y = -2x +6, or y = (-1\/3) x +1.\u00a0 The product of the slopes, 3 (-1\/3) = -1.<\/p>\n

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Overview Parallel lines never intersect when they are graphed on the same plane, while perpendicular lines are lines that intersect at one point at right angles to each other.\u00a0 Their linear equations have special relationships. Parallel Lines Parallel lines are lines in the same plane that have no points in common.\u00a0 Suppose that one line […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2639,1281,1320,1660],"class_list":["post-9025","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-linear-equations","tag-parallel-lines","tag-perpendicular-lines","tag-slope"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=9025"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9025\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=9025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=9025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=9025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}