X and Y Intercept Calculator

The X and Y Intercept Calculator finds where a line — written as ax + by + c = 0 — crosses the x-axis and y-axis. Enter the three coefficients and it returns both intercept points, the slope, a plain-English classification (horizontal, vertical, or oblique), and a step-by-step derivation.

It's built for algebra students, teachers preparing worked examples, and anyone who needs a line's intercepts without rearranging the equation by hand.

How to use it

1. Enter a — the coefficient of x.
2. Enter b — the coefficient of y.
3. Enter c — the constant term.
4. Read the X-Intercept and Y-Intercept fields, or Step-by-Step Derivation for the full working.

Results update automatically as you type. For example, entering a = 2, b = 3, c = -6 returns an x-intercept of (3, 0) and a y-intercept of (0, 2).

How are the intercepts found?

The x-intercept is the point where the line crosses y = 0, so setting y to 0 in ax + by + c = 0 and solving gives x = -c/a. The y-intercept works the same way in reverse: setting x to 0 gives y = -c/b. The slope follows directly from the same equation: m = -a/b.

What if a or b is 0?

• a = 0 — there's no x term, so the line is horizontal: it has a y-intercept but never crosses the x-axis (unless the line sits exactly on it).
• b = 0 — there's no y term, so the line is vertical: it has an x-intercept but never crosses the y-axis (unless the line sits exactly on it), and its slope is undefined.
• a and b both 0 — there's no line to solve for, so the calculator flags this as invalid input.

For solving a one-variable linear equation directly, see the Linear Equation Solver. To build a line's equation from a point and a slope instead, see the Point-Slope Form Calculator.

Privacy

This calculator runs entirely in your browser. Your coefficients are never uploaded, logged, or stored — the computation happens locally on your device.