### Let’s Think About It

Mary Ellen has $60 to spend at the craft store and she is very interested in buying either scrapbooks that cost $10 or fashion stickers that cost $5 per package. Before making a purchase, she needs to know how many scrapbooks or how many packages of stickers she can buy with her money. How can Mary Ellen figure this out?

In this concept, you will learn to use intercepts.

### Guidance

Consider the following linear graph.

The above graph models the linear function **intercept**. The -value of any point on the -axis is zero. The -axis is really the line having the equation .

The line also passes through the -axis at the point **intercept**. The -value of any point on the -axis is zero. The -axis is really the line having the equation .

Remember, only two points are needed to draw a straight line. Therefore, the graph of the linear function intercepts and using a straight edge to join the two plotted points.

was drawn by plotting the - and -From a given function, the intercepts can be determined using algebra. Let’s look at an example.

First, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘5’ to solve for ‘’.

The answer is 3.

The

-intercept is .Second, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘-3’ to solve for ‘’.

The answer is -5.

The

-intercept is .Now, the values of the

- and -intercepts can be used to plot the graph of the linear function .

### Guided Practice

For the given linear function, determine the

- and -intercepts.

First, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘4’ to solve for ‘’.

The answer is -6.

The

-intercept is .Second, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘-3’ to solve for ‘’.

The answer is 8.

The

-intercept is .### Examples

#### Example 1

For the given linear function, use the

-and -intercepts to draw the graph:

First, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by

to solve for ‘’.

The answer is 4.

The

-intercept is .Second, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘-4’ to solve for ‘’.

The answer is -6.

The

-intercept is .Now, the values of the

- and -intercepts can be used to plot the graph of the linear function.

#### Example 2

For the following graph, name the

- and -intercepts.

The graph crosses the

-axis at the point and the -axis at the point .The

-intercept is and the -intercept is .#### Example 3

For the given linear function, determine the

- and -intercepts.

First, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘15’ to solve for ‘’.

The answer is 8.

The

-intercept is .Second, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘30’ to solve for ‘’.

The answer is 4.

The

-intercept is .### Follow Up

Remember Mary Ellen and the scrapbooks or stickers? She needs to figure out how many scrapbooks or how many packages of fashion stickers she can buy with her $60.00. How can she do this?

Mary Ellen can use the

- and -intercepts of a linear function.First, write a linear function to represent the information given.

Let ‘’ represent the number of scrapbooks that cost $10 each and let ‘’ represent the number of packages of stickers that cost $5.00 each. She has $60.00 to spend.

The linear function to model the given information is:

Next, determine

- and -intercepts of the linear function.First, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘10’ to solve for ‘’.

The answer is 6.

The

-intercept is .Second, determine the

-intercept. Substitute in the equation.

Next, perform the multiplication to clear the parenthesis.

Next, divide both sides of the equation by ‘30’ to solve for ‘’.

The answer is 12.

The

-intercept is .Mary Ellen can buy either 6 scrapbooks and no stickers or 12 packages of stickers and no scrapbooks.

### Video Review

https://www.youtube.com/watch?v=xGmef7lFc5w

### Explore More

Determine the and

-intercepts of each equation. There will be two answers for each equation.1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Look at each graph and identify the

and -intercept of each equation. Each graph will have two answers.11.

12.

13.

14.

15.