Finding the zero of a linear function is easy if you can find the x-intercept. The zero is the x-value of the x-intercept.

Let’s look at this example. What is the zero of the function five-fourths 5 4 y = -5x + 15?

Hint (solving for x-intercept/zero):

Sketch and label an x-intercept so you can remember what it means.
See example on right.

Because you are solving for an x-intercept, plug in 0 for y and solve.

When given an equation, you can double check your answer on the graphing calculator if you solve for y. See Module 1, lessons 9 and 10 for solving for y.

Solve for zero like this:

Use the graphing calculator like this:

Change the equation to slope-intercept form and type it into the equation editor (Y=) as y = -4x + 12. In the graph screen, click TRACE and type in your answer and press enter. Or in the table, you can look for the x-value with y = 0.

So, what is the zero of the function five-fourths 5 4 y = -5x + 15?

Interactive popup. Assistance may be required.

Check Your Answer

Both the equation and the graphing calculator show the zero of this function is 3.