How to Find the X Intercept of a Function

By Michael Keenan
A calculator can assist with determing the x-intercept.

The x-axis is the horizontal axis on a graph, and the y-axis is the vertical axis. The x-intercept is the point a line, represented by a function, where it crosses the x-axis on the graph. The x-intercept is written as (x, 0), because the y-coordinate is always zero at the x-intercept. If you know the slope and the y-intercept of the function, you can calculate the x-intercept using the formula (y - b) / m = x, where m equals the slope, y equals zero, and b equals the y-intercept.



Substitute the known slope for m and the y-intercept for x in the equation (y - b) / m = x. For example, if the slope equals 5 and the y-intercept equals 3, write the formula as (y - 3) / 5 = x.

Substitute 0 for y in the equation, since the value of y is zero In this example at the x-intercept. Using the previous example, (y - 3) / 5 = x, the equation becomes (0 - 3) / 5 = x.

Solve the equation for the value of x. Using the previous example, (0 - 3) / 5 = x, solve the numerator first. Subtract 0 from 3 to get negative three. The result is -3 / 5 = x. Convert the fraction to a decimal by dividing -3 by 5, and the result is -0.6. The x-intercept equals -0.6.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."