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 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.
Finding the Intercepts
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.
Using Intercepts to Graph a Line
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.
Applications of Intercepts
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.
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