{"id":8743,"date":"2015-10-04T21:08:36","date_gmt":"2015-10-04T21:08:36","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8743"},"modified":"2015-10-05T22:48:29","modified_gmt":"2015-10-05T22:48:29","slug":"math-review-of-transforming-linear-functions","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-transforming-linear-functions\/","title":{"rendered":"Math Review of Transforming Linear Functions"},"content":{"rendered":"

Overview<\/h3>\n

The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = mx + b.<\/p>\n

Family of Functions<\/h3>\n

The graphs of linear functions all have the same basic shape: a line. They form a family because they all follow that basic shape and their lines express the same equation, y = mx + b, the slope-intercept form. The most basic function in the family, f(x) =x, is called the parent function.<\/p>\n

Translation<\/h3>\n

One line can be translated to another line if the y-intercept is changed. Since the slopes of the lines are still the same, but they cross the y axis at different points, they are parallel. Suppose one line has the equation y = x + 3 and another line has the equation y = x – 2. The slope of the line x is the same for both lines, but one crosses the y axis at 3, while the other crosses the y axis at -2. It is as if the entire line with the equation y = x + 3 slid down to fit in the position y = x – 2. The line y = x is parallel to the other two, as the slope x is still the same, but the y intercept is at the origin.<\/p>\n

\"\"<\/a><\/p>\n

Rotation<\/h3>\n

Graphs of lines can also be changed so they have the same y intercept, but different slopes. The line may have a steeper slope or one that is less steep. It is as if the entire line were turned. For example, lines of direct variation have the same y-intercepts but different slopes. All the lines may have their y intercepts at the origin, but the line y = -3x is steeper than the line y = 2x, and the line y = x is not quite as steep.<\/p>\n

\"\"<\/a><\/p>\n

Reflection<\/h3>\n

Remember that the reflection of a figure is its opposite across a line of symmetry. The reflection of a line is similar to the reflection of a figure, as it represents its mirror image. If a line has slope m, its reflection will have a slope multiplied by -1. Suppose a line can be represented by the equation y = 3x. Its reflection will have the slope (3) (-1), or -3.<\/p>\n

\"\"<\/a><\/p>\n

Interested in math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

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 Knoxville, TN: visit: Tutoring in Knoxville, TN<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = mx + b. Family of Functions 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":[1046,1508,1560,1845],"class_list":["post-8743","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-linear-functions","tag-reflection","tag-rotation","tag-translation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8743","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=8743"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8743\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8743"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8743"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}