{"id":8978,"date":"2016-06-07T04:14:44","date_gmt":"2016-06-07T04:14:44","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8978"},"modified":"2016-06-07T04:14:44","modified_gmt":"2016-06-07T04:14:44","slug":"math-review-of-linear-equations-and-slope","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-linear-equations-and-slope\/","title":{"rendered":"Math Review of Linear Equations and Slope"},"content":{"rendered":"

Overview<\/h3>\n

Linear equations can be graphed by using intercepts or by changing the equation to standard form to make it easier to graph. \u00a0Horizontal and vertical lines have special relationships in terms of the standard form.\u00a0 The slope of a line is a ratio that describes the steepness and direction of the line.<\/p>\n

Graphing by Using Intercepts<\/h3>\n

Often, the easiest way to graph a line on the Cartesian coordinate system is by using the points where the line crosses the x axis and the y axis.\u00a0 The x-intercept of a line is the x coordinate of the point where the line intercepts the x axis.\u00a0 The y-intercept of a line is the y coordinate of the point where the line intercepts the y axis.\u00a0 For example, in the graph below, the x coordinate of the x intercept is -4 and the y coordinate of the y-intercept is 6.\u00a0 Notice that the y coordinate of the x intercept is 0 and the x coordinate of the y intercept is 0.<\/p>\n

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Standard Form of Linear Equations<\/h3>\n

The standard form of a linear equation is the form ax +by = c, where a, b, and c are constants and either a or b can be zero, but not both of them in the same equation.\u00a0 An equation such as 3x +4y = 12 is already in standard form, because 3, 4, and 12 are all constants.\u00a0 An equation such as 2y = 3x \u2013 6 is not in standard form, but it can easily be put into standard form as 2y \u2013 3x = -6.<\/p>\n

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Horizontal and Vertical Lines<\/h3>\n

The equations of horizontal lines have a special relationship to standard form.\u00a0 Suppose the equation is y =4.\u00a0 How can that be put in standard form?\u00a0 The coefficient of x is 0, or 0x +y = 4.\u00a0 Any value of the x coefficient is possible as long as y equals 4.\u00a0 Any ordered pair will be a solution to the equation y=4 as long as y is 4, so (-32, 4) (-9, 4) (0, 4) and so on are all points along that line.\u00a0 Similarly, suppose the equation is x =-5.\u00a0 This time, any value of the y coefficient is possible as long as x equals -5.<\/p>\n

Slope<\/h3>\n

The slope of a line is a ratio that describes the steepness and direction of the line.\u00a0 It is defined as the change in the y coordinates or the rise, divided by the change in the x coordinates or the run.\u00a0 Suppose a line contains the points (1, 2) and (4, 3).\u00a0 The change in the y coordinates (\u0394y) can be expressed as 3-2 or 1, and the change in the x coordinates (\u0394x) can be expressed as 4-1 or 3.\u00a0 Rise\/run is 1\/3.<\/p>\n

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Overview Linear equations can be graphed by using intercepts or by changing the equation to standard form to make it easier to graph. \u00a0Horizontal and vertical lines have special relationships in terms of the standard form.\u00a0 The slope of a line is a ratio that describes the steepness and direction of the line. Graphing by […]<\/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":[3953,2639,1660,3954],"class_list":["post-8978","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-intercepts","tag-linear-equations","tag-slope","tag-standard-form"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8978","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=8978"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8978\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}