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Horizontal and Vertical Intercepts

The points where a line crosses the vertical and horizontal axes are known as the vertical and horizontal intercepts. (These points are often referred to as the x-intercept and the y-intercept.) Given a linear function f(x) = mx + b,

  1. The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function.
  2. The horizontal intercept  (x-intercept) is the value of the variable x when the function value is 0. It is found by solving the equation  0= mx + b.

Interactive Example

Now explore how the values of the y-intercept, b, affect the graph of the linear function y = mx + b.

Algebraic Example

Find the vertical and horizontal intercept of the linear function .


 Since f(0) = -7.2(0) + 250 = 250, the vertical intercept is 250. This means that the graph of the linear function crosses the horizontal axis at the point (0, 250). Also notice that this is the value of b in the linear function f(x) = mx + b.

To find the horizontal intercept we can replace f(x) with 0 and solve the linear equation  The solution is given below. 

The horizontal intercept is 34.7. This is the point (34.7, 0) on the graph of the linear function. A graph of the linear function is shown in Figure 2.

            Figure 2