{"id":8668,"date":"2015-08-21T05:43:24","date_gmt":"2015-08-21T05:43:24","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8668"},"modified":"2015-08-21T14:05:21","modified_gmt":"2015-08-21T14:05:21","slug":"math-review-of-linear-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2015\/08\/21\/math-review-of-linear-functions\/","title":{"rendered":"Math Review of Linear Functions"},"content":{"rendered":"

Overview<\/h3>\n

In order for functions to be linear, they must follow two criteria. First, each domain value must be paired with one range value. If a domain value is paired with more than one range value, the relationship is not a function. Second, the paired domain and range values must fall on a line to be a linear function.<\/p>\n

Identifying Functions<\/h3>\n

In order for a relationship to be a function, each domain value (x) must be paired with a range value (y). Suppose that a particular set has ordered pairs of {(4, -4) (3,-2) (2, 0) (1, 2)}. The domain values are (4, 3, 2, 1) paired with range values of (-4, -2, 0, 2). It is a function. Another set has values of { (3, 0) (3, 1) (3, 2) (3, 3)}. It is not a function, because the domain value 3 is paired with different range values (0, 1, 2, 3).<\/p>\n

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Linear Functions<\/h3>\n

For functions to be linear, the change in the domain values must be constant and the change in the range values must also be constant. The set with ordered pairs {(4, -4) (3, -2) (2, 0) (1,2)} has a constant change in the domain values, as 4-1 is 3, 3-1 is 2, and 2-1 is 1. It also has a constant change in the range values as -4 +2 is -2, -2 +2 is 0, and 0 +2 is 2. Not all functions are linear, however. A set such as {(-2, 6) (-1, 3) (0, 2) (1, 3) (2, 6)} is a function, with a constant change in the domain values, as -2 +1 is -1, -1 +1 is 0, 0 +1 is 1, and 1 +1 is 2. The change in the range values is not constant, as 6-3 is 3, 3-2 is 1, 2 +1 is 3, and 3 +3 is 6.<\/p>\n

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Standard Linear Equation<\/h3>\n

Linear equations can be written in a standard form ax + by = c, where a, b, and c are all real numbers, and a and b are not both 0. Notice that this means that either a or b can be 0. For example, an equation such 3x +5y = 16 is already in standard form, as a equals 3, b equals 5, and c equals 16. Similarly, an equation such as y = 5x \u2013 3 can be put in standard form as -5x +y =-3.<\/p>\n

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Graphing Linear Functions<\/h3>\n

If the equation for a function can be written in standard form, it can be graphed as a linear function. Suppose the equation is 2x +3y = 20. It is already in standard form, as a =2, b =3, and c =20. If x equals 1, then y equals 6, if x equals 4, then y equals 4, and if x equals 7, then y equals 2.<\/p>\n

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Overview In order for functions to be linear, they must follow two criteria. First, each domain value must be paired with one range value. If a domain value is paired with more than one range value, the relationship is not a function. Second, the paired domain and range values must fall on a line to […]<\/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":[540,3813,1481,3814],"class_list":["post-8668","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-domain","tag-linear-function","tag-range","tag-standard-linear-equation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8668","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=8668"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8668\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}