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Point-Slope Form

If you know the slope $m$ of a line and the coordinates $\left(x_1,y_1\right)$ of one point on the line, you can write the equation of the line in point-slope form.

$y-y_1=m\left(x-x_1\right)$

Here, $m=-\frac{1}{2}$ , $x_1=-3$ , and $y_1=2$ , so the equation is:

$y-2=-\frac{1}{2}\left(x-\left(-3\right)\right)$

or

$y-2=-\frac{1}{2}\left(x+3\right)$

Slope-intercept form is a special case of point-slope form, where we use the $y$ -intercept coordinate $\left(0,b\right)$ as our point.