Find X- and Y-Intercepts with the worked examples below. Start by locating the horizontal and vertical axes. Record each intercept as an ordered pair so you can distinguish the x-coordinate from the y-coordinate.
Find X- and Y-Intercepts step by step
For y = 3x − 9, try x = 0 first. That gives (0, −9). To find the other intercept, solve 3x − 9 = 0. The result is (3, 0).
Common mistake to watch for
The line y = 4 never meets the x-axis. It meets the y-axis at (0, 4). The function y = x² + 1 also has no real x-intercepts because its minimum y-value is 1.
Practice problem with answer
Plot y = x² − 9. Predict how many times it meets each axis, then verify the x-intercepts at (−3, 0) and (3, 0) and the y-intercept at (0, −9).
Check your result with the online graphing calculator. Continue with How to Find the Intersection of Two Graphs or see the Desmos graphing guide.
GRAPHING GUIDE
Start with the graph
An x-intercept is a point where y equals zero. A y-intercept is a point where x equals zero. The origin can be both.
Worked example
Plot y = 2x − 6. Find where the line meets each axis. Setting y = 0 gives 2x = 6, so the x-intercept is (3, 0). Setting x = 0 gives the y-intercept (0, −6).
Try another example
Plot y = x² − 4. The x-intercepts are (−2, 0) and (2, 0), while the y-intercept is (0, −4). A curve may touch the x-axis without crossing it, as y = x² does at the origin.
Check your result
Check that the viewing window includes both axes. If a crossing looks approximate, substitute its coordinate into the original equation.
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