# What is the slope of any line perpendicular to the line passing through (-3,-12) and (5,-3)?

Dec 12, 2015

$- \frac{8}{9}$

#### Explanation:

A line perpendicular to another line has an OPPOSITE RECIPROCAL slope.

For example, if a line had a slope of $2$, the perpendicular line's slope would be $- \frac{1}{2}$.
Similarly, a line with slope $- \frac{3}{5}$ would be perpendicularly intersected by a line with a slope of $\frac{5}{3}$.

To find the slope of the perpendicular line, first find the slope of the original line.

$\text{slope} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$= \frac{- 3 - \left(- 12\right)}{5 - \left(- 3\right)} = \frac{- 3 + 12}{5 + 3} = \frac{9}{8}$

The perpendicular line's slope will be the opposite reciprocal of $\frac{9}{8}$, which is $- \frac{8}{9}$.