Slope–Intercept Form

m is the slope, c is the y-intercept. Every non-vertical line can be written in this form.

Derivation

Every non-vertical line cuts the $y$ -axis at exactly one point. Call it $(0, c)$ — the $y$ -intercept.

The line has slope $m$ , so for any other point $(x, y)$ on it:

\frac{y - c}{x - 0} = m

Multiply through by $x$ :

\boxed{y = mx + c}

This is a special case of the point-slope form with base point $(0, c)$ .

Note

Every non-vertical line has a unique slope-intercept form. Vertical lines ($x = k$) cannot be written this way — the slope is undefined.