Standard Form to Slope Intercept Form Calculator

Standard Form vs Slope-Intercept Form

A linear equation can be written in standard form $Ax + By + C = 0$ or in slope-intercept form $y = mx + b$. Standard form is useful for systems of equations and geometry, while slope-intercept form makes the slope $m$ and y-intercept $b$ immediately visible. This calculator converts between both forms with step-by-step algebra.

For related tools, see the Equation of a Line Calculator and Slope Calculator.

Conversion Formulas

From standard form to slope-intercept (when $B \neq 0$):

$$y = -\frac{A}{B}x - \frac{C}{B}$$

So $m = -\frac{A}{B}$ and $b = -\frac{C}{B}$.

From slope-intercept to standard form:

$$mx - y + b = 0$$

Worked Example

Convert $2x - 3y + 6 = 0$ to slope-intercept form. Isolate $y$:

$$-3y = -2x - 6 \Rightarrow y = \frac{2}{3}x + 2$$

The slope is $\frac{2}{3}$ and the y-intercept is $2$.