Converts a line’s equation from standard form (Ax + By = C) into slope-intercept form (y = mx + b).
How it works
The equation is algebraically rearranged: the slope equals negative A divided by B, and the y-intercept equals C divided by B.
What this does not include
This does not include converting from two points or a point-and-slope — for those, use this site’s slope-intercept form or point-slope form calculators instead.
How to use this calculator
- Enter the A, B, and C coefficients from the standard-form equation.
A worked example
Standard form 2x + 4y = 8: solving for y gives slope-intercept form y = −0.5x + 2 — slope −0.5, y-intercept 2.
3x − 2y = 6: y = 1.5x − 3.
What the variables mean
| Variable | Meaning |
|---|---|
| a, b, c | Coefficients of standard form ax + by = c |
| Slope, intercept | The m and b values in slope-intercept form y = mx + b |
Edge cases worth knowing
A b coefficient of zero means a vertical line, which has no slope and can’t be written in y = mx + b form at all — the calculator declines to show a result for that case.
The sign of a/b determines whether the slope is positive or negative — flipping the sign of either coefficient flips the line’s direction.
Frequently asked questions
What happens if B is zero?
The equation represents a vertical line, which has no slope-intercept form (an undefined slope) — this calculator declines to return a result in that case.
Why is the slope negative A over B?
It falls directly out of rearranging Ax + By = C to solve for y — dividing both sides by B and isolating y produces that exact ratio.
Does the resulting equation represent the same line?
Yes — slope-intercept form is just a different way of writing the identical line, rearranged for easier graphing.
