How to Locate X-Intercepts

Knowing how to locate X-Intercepts can help you to read a graph.

X and Y intercepts are graphical points used in algebra. The X intercept is always the point on a Cartesian graph where Y is zero, meaning that the line sits directly on the X axis at this point. You can locate the X intercept in a given problem in one of two ways, depending on the problem. You may be presented with a graph or an equation. In either case, locating the X intercept is a relatively basic procedure.

Instructions

1. Locate the X axis if you are given a graph on which to locate the X intercepts. This is the line which runs horizontally through the graph.

2. Follow the X axis across the graph and note any points where the line on the graph crosses the X axis. The points to the right of the vertical Y axis are positive numbers, beginning with one as the closest number to the Y axis, and continuing upward. The points to the left of the Y axis are negative, beginning with -1 and continuing downward. The points where the line crosses the X axis are the X intercepts.

3. Examine the equation you are given if no graph is provided for locating the X intercept. The equation will have both an X and a Y in it. An example of one such equation would be 2x -- 3y = -6

4. Set Y to zero. For the above example, this would make the equation 2x -- 3(0) = -6. Further simplified this is 2x = -6.

5. Solve the equation for the value of x. For the previous example, you would need to divide -6 by 2 to eliminate the 2 from the x side of the equation. This leaves you with x = -3. Therefore, -3 is the X intercept in this case.

References

• College Algebra Tutorial: x-Intercepts and y-Intercepts
• Purple Math: x- and y-Intercepts