What are intercepts and how do you find them?

Intercepts are where a

graph crosses either the

x-axis or the y-axis. Not all functions will have intercepts, but when you are working with the

graph of a linear function, it will have both an

x-intercept and a y-intercept. An

x-intercept is where the

graph crosses the

x-axis and a

y-intercept is where it crosses the y-axis.

Let’s think about a

line that crosses the x-axis. If it is crossing the x-axis, then the y-value of that

point will be zero. Similarly, when dealing with the y-intercept, this is where the x-value is zero. We will use this information in finding x-and y-intercepts.

The **general rules** are: - To find an x-intercept, let the value of y in the equation be equal to zero.

Your x-intercept will be written as a point .

- To find a y-intercept, let the value of x in the equation be equal to zero.

Your y-intercept will be written as a point .

**Let's Practice:**- Find the x- and y-intercepts for .

The y-intercept is found by letting x = 0. We write the y-intercept as ,

The x-intercept is found by letting y = 0. We write the x-intercept as .

You may have noticed something interesting about the

y-intercept in the previous example. The

y-intercept was the number by itself in the

equation of the line. The

equation in Example 1 is called the

slope-intercept form of a

line and in general is written as

. In this equation, the

slope of the

line is

*m* and the

y-intercept is

*b*. You can learn more about finding the

slope of a

line by

clicking here. This slope-intercept form of a

line makes is easy to find the y-intercept.

**More Practice:**- Find the x-and y-intercepts for

Since this equation is in slope-intercept form, we can find the y-intercept by looking at the equation. The y-intercept is 4 and is written as .

To find the x-intercept, let y = 0 in the equation. The x-intercept is written as .

- Find the x-and y-intercepts for .

This equation is not in slope-intercept form, so we go back to our strategy of substituting x = 0 to find the y-intercept. The y-intercept is . To find the x-intercept, let y = 0. The x-intercept is .

There are two special types of lines that need to be considered when talking about intercepts. These are horizontal lines and vertical lines.

- A horizontal line is in the form y = k; that is,

no matter what the x-value is, the y-value is always a constant value.

- A vertical line is in the form x = h; that is,

no matter what the y-value is, the x-value is always a constant value.

**Final Practice:**- Consider the graph of y = 3.

The horizontal line shown in this graph will never cross the x-axis. A horizontal line (other than y = 0) will not have an x-intercept. The line y = 0 is another special case since y = 0 is the equation of the x-axis.

The y-intercept will always be the number in the equation. So in this case, .

- Consider the graph of x = -4.

The vertical line shown in this graph will cross the x-axis at the number given in the equation. For this equation, the x-intercept is .

Notice this line will never cross the y-axis. A vertical line (other than x = 0) will not have a y-intercept. The line x = 0 is another special case since x = 0 is the equation of the y-axis.

Now that you have these tools to find the intercepts of a line, what does this information do for you? What good are intercepts other than just knowing points on a graph?

The x-and y-intercepts play a key role in graphing linear functions. To learn more about graphing lines,

click here.