{"id":8700,"date":"2015-09-06T18:21:00","date_gmt":"2015-09-06T18:21:00","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8700"},"modified":"2015-09-09T16:17:33","modified_gmt":"2015-09-09T16:17:33","slug":"math-review-of-intercepts","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-intercepts\/","title":{"rendered":"Math Review of Intercepts"},"content":{"rendered":"

Overview<\/h3>\n

A linear function follows the standard form ax + by = c. The intercepts are the points where the line intersects each axis. A line can be graphed by connecting the intercepts.<\/p>\n

Definitions<\/h3>\n

The y-intercept is the point at which the line intersects the y axis. At the y axis, the value of x is zero. However, the x intercept is the point at which the line intersects the x axis. At the x axis, the value of y is zero. Suppose a linear function is drawn so that the y intercept is at (0, 3). The value of x is 0 and the value of y is 3. Without defining the x intercept, an infinite number of lines could be drawn through the y intercept. However, this particular line has an x intercept at (4, 0). The value of x is 4 and the value of y is 0.<\/p>\n

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Finding the Intercepts<\/h3>\n

The definition of the y intercept is the value of x is 0, and the definition of the x intercept is the value of y is 0. In order to find the x and y intercepts in an equation such as 3x + 4y = 12, find the value of x when y equals 0, and the value of y when x equals 0. To find the x intercept for this equation, the y value must equal 0. Therefore, 3x + 4(0) = 12, or 3x = 12, or x = 12\/3, or x = 4. To find the y intercept, the x value must equal 0. Therefore, 3(0) + 4y = 12 or 4y = 12, or y = 12\/4, or y equals 3.<\/p>\n

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Using Intercepts to Graph a Line<\/h3>\n

If the equation is linear, it can be graphed by using the intercepts. For example, if a function has x intercept 4 and y intercept 2, two of the points on the line will have the values (4, 0) and (0, 2). Plot a line through those two Cartesian coordinates to graph the line. Check to see if another point on the line is a solution to the equation, either by choosing a point on the graphed line, or by calculating another value from the equation and checking to see if it is also on the graphed line.<\/p>\n

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Applications of Intercepts<\/h3>\n

The x intercept and y intercept can be used in real-world applications. Suppose a vehicle is traveling at a constant speed. A linear function can be graphed representing its distance from its destination (y) vs the time traveled (x). The y intercept represents the maximum distance and the x intercept represents the maximum amount of time traveled, when the vehicle reaches its destination.<\/p>\n

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Overview A linear function follows the standard form ax + by = c. The intercepts are the points where the line intersects each axis. A line can be graphed by connecting the intercepts. Definitions The y-intercept is the point at which the line intersects the y axis. At the y axis, the value of x […]<\/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":[3460,3462],"class_list":["post-8700","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-x-intercepts","tag-y-intercepts"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8700","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=8700"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8700\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}