🎯 Intercepts Calculator
The intercepts are the two points where a line crosses the axes — the x-intercept where it meets the x-axis (y = 0) and the y-intercept where it meets the y-axis (x = 0). They are the fastest way to sketch a line, and the standard form Ax + By = C makes them almost trivial: divide C by A and by B.
Enter A, B and C and this calculator returns both intercepts as points, the slope, and the slope-intercept form, with the line and both crossing points drawn for you.
How to use this calculator
Set y = 0 to get the x-intercept and x = 0 to get the y-intercept — the calculator does both, instantly.
- Write your line as Ax + By = C and type A, B and C.
- Press Calculate.
- Read the x-intercept (C/A, 0) and y-intercept (0, C/B).
- Use the two points to sketch the line — or check the drawn graph.
Intercepts Worked Example
Find the intercepts of 2x + 3y = 6. For the x-intercept set y = 0: 2x = 6, so x = 3 → the point (3, 0). For the y-intercept set x = 0: 3y = 6, so y = 2 → the point (0, 2). Joining those two points draws the whole line, whose slope is −2/3. These are the default values above.
Frequently asked questions
How do you find the x and y intercepts from standard form?
From Ax + By = C: the x-intercept is C/A (set y = 0) and the y-intercept is C/B (set x = 0). Two divisions give you two points, and two points define the line — that is why standard form is so convenient.
Can a line have no x-intercept or no y-intercept?
Yes. A horizontal line like y = 4 never crosses the x-axis, so it has no x-intercept. A vertical line like x = −2 never crosses the y-axis. A line through the origin has both intercepts at the same point, (0, 0).
What is the difference between an intercept value and an intercept point?
Strictly, the intercepts are points: (3, 0) and (0, 2). In everyday use people often quote just the non-zero coordinate ("the y-intercept is 2"). This calculator gives the full points so there is no ambiguity.
Why is the y-intercept important in real problems?
In slope-intercept form y = mx + b, b is the starting value before anything changes: the fixed fee before per-kilometre charges, the balance before interest, the height before growth. It is the value of the situation at x = 0.