How this calculator works
Every point on the y axis has x = 0. Substitute that value into a line equation to isolate the y-intercept. A point and slope give the same result by moving from the point back to x = 0. A vertical line away from the axis never meets it, while the y axis itself contains infinitely many intersections. Those cases receive a status message rather than an invented numeric intercept.
Formula
For y = mx + b, the y-intercept is b. For Ax + By = C and B nonzero, b = C/B and m = -A/B. Through (x0,y0), b = y0 - mx0. If m is nonzero, x-intercept = -b/m.
Worked example
For 2x + 3y = 12, setting x = 0 gives y = 4. The slope is -2/3 and the x-intercept is 6. A line through (2,5) with slope 3 instead has intercept 5 - 3 x 2 = -1.
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Frequently asked questions
Can the intercept be negative?
Yes. A negative intercept means the line crosses the y axis below the origin.
What if my equation uses Ax + By + C = 0?
Move the constant to the other side and enter its negative in the C field, which uses Ax + By = C.
Does a horizontal line have an x-intercept?
A nonzero horizontal line never reaches the x axis. The line y = 0 lies on it, so every x is an x-intercept rather than one unique value.