How to Find X-Intercept

By Joe White

Cartesian planes, the graphs on them and the equations that define those graphs are a basic element of algebra and more advanced mathematics. The standard form for those equations is y=mx+b; this is called the slope-intercept form. A first operation that is necessary for many more complex problems is to find the intercepts of the function. The intercepts are simply the points on the Cartesian plane where the graph crosses the axes. Algebraically, the intercepts are defined by values of the function where x=0 or y=0.

Step 1

Determine the format of the equation you are dealing with. If you have the standard slope-intercept form, then the X-intercept is listed already. For example, in the equation y=3x-4, the X-intercept is -4.

Step 2

Set the x value to zero and solve for y. This way, no matter what form the equation is written in, you will find the y value when x=0, which is the X-intercept.

Step 3

Set x=0 in point slope form as well, when the function is defined in the form (y-Y)=m(x-X).

Step 4

Solve for y. In the equation (y-2)=4(x-1), when we substitute 0 for x, we are left with y-2=4(0-1). Therefore y-2=4(-1); therefore y-2=-4; therefore y=-4+2; therefore y=-2; the X-intercept is -2.