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# Intercepts of a Line

Example

Given the equation 4x - 3y = 12:

a. Find the x-intercept.

b. Find the y-intercept.

c. Use the intercepts to graph the line.

 a. Solution The x-intercept has the form (a, 0). To find the x-intercept, substitute 0 for y. Then solve for x. Simplify. Divide both sides by 4. The x-intercept is (3, 0). 4x - 3y 4x - 3(0) 4x x = 12 = 12 = 12  = 3 b. The y-intercept has the form (0, b). To find the y-intercept, substitute 0 for x. Then solve for y. Simplify. Divide both sides by -3. The y-intercept is (0, -4). 4x - 3y  4(0) - 3y  -3y y = 12 = 12 = 12 = -4 c. To graph the line 4x - 3y = 12, plot the x-intercept and the y-intercept. Then, draw a line through the intercepts. As a check, it is a good idea to find a third point on the line. For example, choose 6 for x in the equation 4x - 3y = 12. Solve for y. The result y = 4. Since (6, 4) is a solution of the equation 4x - 3y = 12, the line should pass through the point (6, 4).
 x y 3 0 x-intercept 0 -4 y-intercept 6 4 check point

Some lines do not have both an x-intercept and a y-intercept.

â€¢ A horizontal line, other than the x-axis, has a y-intercept, but no x-intercept.

For example, the horizontal line y = 6 has y-intercept (0, 6), but no x-intercept.

â€¢ A vertical line, other than the y-axis, has an x-intercept, but no y-intercept.

For example, the vertical line x = 2 has x-intercept (2, 0), but no y-intercept.

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