How do you find the x-intercept of a line?

The x-intercept is the point where a graph crosses the x-axis. Every point on the x-axis has y equal to zero, so finding the x-intercept means setting y to zero and solving for x. The answer is normally written as a coordinate with the form (x, 0).

For a line in slope-intercept form, y = mx + b, replace y with zero. The equation becomes 0 = mx + b, so x = -b/m as long as m is not zero. For example, if y = 3x - 12, then 0 = 3x - 12, which gives x = 4. The x-intercept is (4, 0). I substitute that point back into the original equation to confirm it works.

If the equation is presented in standard form, Ax + By = C, set y to zero and solve Ax = C. This gives x = C/A when A is not zero. A vertical line such as x = 5 crosses the x-axis at (5, 0). A horizontal line with a nonzero y-value has no x-intercept because it never reaches y = 0.

A graph is a helpful visual check. The line should pass through the calculated point, and the crossing should be on the correct side of the origin. An intercept can be negative, so I do not assume the answer must be positive. When the equation has fractions or decimals, clearing denominators first can reduce arithmetic errors.

graphing-calculator.org can display the line and make its intercept easy to compare with the algebraic result. I still show the substitution of y = 0, because that step explains why the calculation finds the x-axis crossing. If the graph and the calculated coordinate disagree, I check signs and parentheses.