As you have seen in previous resources, linear equations can be written in two forms.

general form of a linear equation in slope-intercept form and in standard form

In addition to determining and interpreting intercepts from graphs and tables, you can also determine and interpret intercepts directly from an equation.

To determine an intercept from an equation, substitute 0 and solve for the other variable. x-intercept: (x, 0) y-intercept: (y, 0).

Interactive exercise. Assistance may be required. In the interactives below, drag the steps of solving the equation into the correct order. Use the completed solutions to look for patterns in how you can determine the x-intercept and y-intercept for a linear equation that is given in slope-intercept form.

Pause and Reflect

How can you determine the x-intercept and y-intercept from an equation in slope-intercept form, y = mx + b?

Interactive popup. Assistance may be required.

Check Your Answer

The x-intercept is the point , and the y-intercept is the point (0, b).Close Pop Up

Interactive exercise. Assistance may be required. In the interactives below, drag the steps of solving the equation into the correct order. Use the completed solutions to look for patterns in how you can determine the x-intercept and y-intercept for a linear equation that is given in standard form.

Pause and Reflect

How can you determine the x-intercept and y-intercept from an equation in standard form, Ax + By = C?

Interactive popup. Assistance may be required.

Check Your Answer

The x-intercept is the point , and the y-intercept is the point .Close Pop Up

Practice

Interpret both intercepts in the relationships below.

  1. Maria has a cell phone plan that uses the equation c = 0.55m + 14, where c represents the total cost and m represents the number of minutes used, to determine the amount of her cell phone bill each month, before taxes and fees.

    Interactive popup. Assistance may be required.

    Need a hint?

    Set each variable equal to 0 and solve for the other variable.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    The m-intercept, (-25.45, 0), shows that the fixed monthly charge is approximately equal to the amount of money that 25.45 minutes cost.
    The c-intercept, (0, 14), shows that if Maria does not use her cell phone at all during a month to make calls, she will pay a $14 fixed charge. Close Pop Up
  2. Subkhir has a car loan, and he uses the equation y = 7,500 – 250x, where x represents the number of months that he has been paying the loan and y represents the remaining balance on the loan, to determine his remaining loan balance.

    Interactive popup. Assistance may be required.

    Need a hint?

    Set each variable equal to 0 and solve for the other variable.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    The x-intercept, (30, 0), shows that in 30 months, the remaining balance will be equal to $0, or in other words, Subkhir’s car loan will be paid in full.
    The y-intercept, (0, 7,500), shows that Subkhir initially borrowed $7,500. Close Pop Up
  3. Nimitha buys fruit at her local farmer’s market. This Saturday, oranges cost $2 per pound and cherries cost $3 per pound. She has $12 to spend on fruit. Nimitha can use the equation 2x + 3y = 12, where x represents the number of pounds of oranges and y represents the number of pounds of cherries, to determine how many pounds of each fruit she may purchase.

    Interactive popup. Assistance may be required.

    Need a hint?

    Set each variable equal to 0 and solve for the other variable.Close Pop Up

    Interactive popup. Assistance may be required.

    Check Your Answer

    The x-intercept, (6, 0), shows that if Nimitha buys only oranges, she can buy 6 pounds of oranges.
    The y-intercept, (0, 4), shows that if Nimitha buys only cherries, she can buy 4 pounds of cherries. Close Pop Up