How to Find X-Intercept, Y-Intercept and Intersections

They are the points where a line crosses, or intercepts, the two axes. The y-intercept is on the y-axis, where x = 0; the x-intercept is on the x-axis, where y = 0. For Amy’s journey, y = 200 − 50x, the y-intercept of 200 is her starting distance and the x-intercept of 4 is the hour she arrives.

Set x to 0 and work out y. For y = 200 − 50x, x = 0 gives y = 200, so the y-intercept is 200. When the equation is in the form y = mx + c, the y-intercept is simply c: for y = 3x + 2 it is 2. On a graph it is where the line crosses the y-axis.

Set y to 0 and solve for x. For y = 200 − 50x: 0 = 200 − 50x, so 50x = 200 and x = 4. For y = −4x + 8: 0 = −4x + 8 gives x = 2. The same works for Google’s 3x + 5y + 15 = 0: with y = 0, 3x = −15, so x = −5. On a graph it is where the line crosses the x-axis.

The point where two lines cross. At that point both equations have the same x and the same y, so it is the one pair of values that fits both lines. Amy’s journey, y = 200 − 50x, and Bobby’s, y = 150 − 30x, cross at (2.5, 75): after 2.5 hours both are 75 miles from the theme park.

Two steps, no graph needed. Set the two equations equal and solve for x: 200 − 50x = 150 − 30x, so 50 = 20x and x = 2.5. Then put x into either equation to find y: 150 − 30 × 2.5 = 75. The intersection is (2.5, 75). Reading it off a graph gives the same point, but the algebra is exact.

Either one, because the point lies on both lines, so choose whichever has the easier numbers. For Amy and Bobby, Bobby’s y = 150 − 30x is simpler: 150 − 30 × 2.5 = 75. Amy’s gives the same: 200 − 50 × 2.5 = 75. Using the second equation as a check costs one line and catches mistakes.