{"id":6809,"date":"2014-03-17T16:42:43","date_gmt":"2014-03-17T16:42:43","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6809"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-introduction-to-linear-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/03\/17\/math-introduction-to-linear-equations\/","title":{"rendered":"Math Introduction to Linear Equations"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Linear equations are prevalent in algebra when the relationship between variables and constants can be plotted on a straight line.\u00a0 For example, suppose the equation were 2x = y.\u00a0 If the value for x were 1, the value for y would be 2, or for x were 2, y would be 4, and so forth.<\/p>\n

What Are Linear Equations?<\/strong><\/p>\n

Suppose the equation were 2x – 1 = 7.\u00a0 There is only one value of x that would make the statement true, if x equaled 4, because 2(4) – 1 equals 7.\u00a0 However, if the equation were 2x \u2013 y = 7, there would be many values for x and for y, such that if x equaled 4, then y would equal 1, if x equaled 5, y would equal 2, and so on.\u00a0 Although only 2 points are needed to plot a straight line, it is useful to have a third as a check. \u00a0If x equaled 2, y would equal -3, because 4 \u2013 (-3) would equal 7.<\/p>\n

What Is the Slope of a Line?<\/strong><\/p>\n

The slope of a line is the ratio between the vertical change to the horizontal change, as long as the horizontal change is not equal to 0.\u00a0 Suppose the equation were 2x = y.\u00a0 If x equals 1, y equals 2, if x equals 2, y equals 4 and so forth.\u00a0 The vertical change is 2 and the horizontal change is 1, so the slope is 2\/1.<\/p>\n

Where Does the Line Cross the Y-Axis?<\/strong><\/p>\n

Suppose the equation were 3x \u2013 y = 11.\u00a0 If x were 4, y would be 1, so its coordinates would be (4, 1), and if x were 2, y would be -5, so its coordinates would be (2, -5).\u00a0 What if x were equal to 0?\u00a0 If x were 0, y would be -11, and its coordinates would be (0,-11).\u00a0 The point at which the line crosses the y axis is the point at which x equals 0.\u00a0 It is called the y-intercept.<\/p>\n

What Is the Slope-Intercept Form of a Line?<\/strong><\/p>\n

The slope-intercept form of a line is the equation for the line that contains both the slope and the y-intercept.\u00a0 Suppose the equation were 2x + y = 5.\u00a0 In order to solve for y the equation would be y = -2x + 5.\u00a0 If y were equal to 5, x would equal 0 (the y intercept), and its coordinates would be (0, 5).\u00a0 If y were equal to 1, x would equal 2, and its coordinates would be (2, 1).\u00a0 The slope of the line would be the ratio of the vertical change to the horizontal change or (5-1)\/(0-2) or 4\/-2 or -2.<\/p>\n

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Overview: Linear equations are prevalent in algebra when the relationship between variables and constants can be plotted on a straight line.\u00a0 For example, suppose the equation were 2x = y.\u00a0 If the value for x were 1, the value for y would be 2, or for x were 2, y would be 4, and so […]<\/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":[2639,1660,1661,2640],"class_list":["post-6809","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-linear-equations","tag-slope","tag-slope-intercept-form","tag-y-intercept"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6809","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=6809"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6809\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}