{"id":8999,"date":"2016-06-17T02:10:37","date_gmt":"2016-06-17T02:10:37","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8999"},"modified":"2016-08-01T03:16:26","modified_gmt":"2016-08-01T03:16:26","slug":"math-review-of-slopes-and-intercepts","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-slopes-and-intercepts\/","title":{"rendered":"Math Review of Slopes and Intercepts"},"content":{"rendered":"

Overview<\/h3>\n

If the linear equation for a line has been determined, the slope of that line can be found by solving for any two points on the line. Similarly, the slope-intercept equation can be used to find the y-intercept and graph the line.\u00a0 If any point on a line and the slope are known, the equation for the line can be found.<\/p>\n

Finding Slope<\/h3>\n

In the figure below, the line is shown with a y intercept at (0, 2) and another point at (4, 0). \u00a0Currently, the equation is in the form x +2y =4. \u00a0Solving the equation for y, if 2y = -x +4, then y = -1\/2 x +2, and the coordinates of the y intercept are (0,2) and the slope is -1\/2. \u00a0(The slope is also shown on the figure below.) \u00a0Given a line y =mx +3, use coordinates on the graph to solve for m.<\/span>\u00a0 Notice that the coefficient of x is also 2.\u00a0 Suppose the equation is 2x +3y =7.\u00a0 Then 3y = -2x +7.\u00a0 If x equals -1, then y equals 3, because 3(3) or 9 equals (-2) (-1) +7.\u00a0 If x equals 2, then y equals 1, because 3(1) = -2(2) +7.\u00a0 The change in y is (1-3) or -2 and the change in x is [(2-(-1)] or (2+1) is 3.\u00a0 Therefore, the slope is -2\/3.\u00a0 If the equation 3y = -2x +7 is divided by 3, it then becomes y = (-2\/3) x + (7\/3), so that the coefficient of x is also -2\/3.\"\"<\/a><\/p>\n

Slope-Intercept Equation<\/h3>\n

An equation of the form y = mx +b is called the slope-intercept equation.\u00a0 In the discussion of finding slope from an equation, the coefficient of x, or the value of m, is the same as the slope.\u00a0 What if the value of x is zero?\u00a0 Then the value of mx is also zero, so the value of y is y = 0 +b, or y =b.\u00a0 The coordinates of that point are (0, b).\u00a0 In other words, the value of b is the y-intercept, because when the value of x is 0, the line crosses the y-axis, also known as the y-intercept.<\/p>\n

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Graphing with the Slope-Intercept Equation<\/h3>\n

The equation y = 2x +3 is already in slope-intercept form, so we know that the slope m is equal to 2 and that the y intercept is at b or (0, 3).\u00a0 We will just need one more point to draw the line, so we can go up 2 units to y equals 5 and to the right 1 or x equals 1, so that the coordinates of that point are (1, 5).\u00a0 If x equals 1, then y equals 2 +3 equals 5.<\/p>\n

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Using the Slope-Intercept Equation<\/h3>\n

Suppose that you have a line with a point (3, 1) that has a slope of 2.\u00a0 The slope-intercept equation y = mx +b can be used to find the equation, because you have a value of x, a value of y, and a value of m. Therefore, 1 equals 2(3) +b.\u00a0 The value of b equals -5, so the slope-intercept equation is y =2x-5.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Hamlet, NC: visit:\u00a0 Tutoring in Hamlet, NC<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview If the linear equation for a line has been determined, the slope of that line can be found by solving for any two points on the line. Similarly, the slope-intercept equation can be used to find the y-intercept and graph the line.\u00a0 If any point on a line and the slope are known, the […]<\/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":[1660,3962,1661],"class_list":["post-8999","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-slope","tag-slope-intercept-equation","tag-slope-intercept-form"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8999","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=8999"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8999\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8999"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8999"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8999"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}