{"id":8972,"date":"2016-06-05T21:16:44","date_gmt":"2016-06-05T21:16:44","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8972"},"modified":"2016-06-05T22:55:49","modified_gmt":"2016-06-05T22:55:49","slug":"math-review-of-graphs-and-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/06\/05\/math-review-of-graphs-and-equations\/","title":{"rendered":"Math Review of Graphs and Equations"},"content":{"rendered":"

Overview<\/h3>\n

The location of points in a plane can be identified by plotting them as ordered pairs, using the Cartesian coordinate system.\u00a0 It can be determined whether an ordered pair is the solution to a particular equation.\u00a0 The solutions to a linear equation with two variables can be plotted on a graph as a straight line.<\/p>\n

Cartesian Coordinate System<\/h3>\n

The Cartesian coordinate system is named for the mathematician Rene Descartes, who lived from 1596 to 1650.\u00a0 It was an important discovery because it allowed algebraic equations to be pictured geometrically, and geometric shapes to be defined algebraically.\u00a0 Until that time, algebra and geometry were two separate fields. \u00a0\u00a0The Cartesian coordinate system has an x axis (abscissa) and a y axis (ordinate) that are perpendicular to each other.\u00a0 The axes divide the coordinate plane into 4 regions, or quadrants, as shown in the picture below.<\/p>\n

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Ordered Pairs<\/h3>\n

The location of any point on a plane can be described by its coordinates, or ordered pairs.\u00a0 A point in the first quadrant, numbered (I) above, has both x and y coordinates as positive numbers, for example (4, 3).\u00a0 A point in the second quadrant, numbered (II) above, has x coordinates as negative numbers and y coordinates as positive numbers for example (-2, 1).\u00a0 A point in the third quadrant, numbered (III) above, has both x and y coordinates as negative numbers, for example (-2, -2).\u00a0 A point in the fourth quadrant, numbered (IV) above has x coordinates as a positive number and y coordinates as a negative number for example (3 -1).\u00a0 Notice that the origin has the coordinates (0, 0).\u00a0 The axes are not part of the quadrants, so that any time that either the x or y coordinates are on the axis, the value of that coordinate is zero.\u00a0 Notice on the graph below that one point is at the coordinates (2, 4).\u00a0 That means that in order to read its location, it is 2 to the right and 4 up from the x axis.<\/p>\n

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Graphing Solutions<\/h3>\n

To see whether or not a particular ordered pair is the solution of an equation with 2 variables, try substituting the values of the ordered pair to see if it solves the equation.\u00a0 If the solution is true, the ordered pair is a solution, but if it is false, the ordered pair is not a solution.\u00a0 For example, is (2, 3) a solution of the equation y = 2x +3?\u00a0 Substitute the 2 for x so that y = 4 +3, or y equals 7.\u00a0 In the ordered pair, y equals 3, so it is not a solution.\u00a0 Is (-2, 4) a solution of 4y \u2013 3x =22.\u00a0 Substitute the -2 for x so that 4y + 6 = 22, so that 4y = 22-6, 4y =16 and y = 4.\u00a0 That statement is true.<\/p>\n

Graphing Linear Equations<\/h3>\n

Linear equations are graphed as straight lines on the Cartesian coordinate system.\u00a0 If the variables are only to the first power, there are no products of variables, and there are no variables in the denominator, then the equation is linear.<\/p>\n

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Overview The location of points in a plane can be identified by plotting them as ordered pairs, using the Cartesian coordinate system.\u00a0 It can be determined whether an ordered pair is the solution to a particular equation.\u00a0 The solutions to a linear equation with two variables can be plotted on a graph as a straight […]<\/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":[3563,3951,3952],"class_list":["post-8972","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-cartesian-coordinates","tag-graphing-linear-equations","tag-ordered-pairs"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8972","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=8972"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8972\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}