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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,*

- 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.
- 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 _{}.

Solution

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