# What is the slope of any line perpendicular to the line passing through (-6,6) and (-2,-13)?

Dec 19, 2016

The slope of any perpendicular line will be: $\frac{4}{19}$

#### Explanation:

First, we need to determine the slope of the line for the two given points.

The slope can be found by using the formula: color(red)(m = (y_2 = y_1)/(x_2 - x_1)
Where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

Substituting the points provided gives:

$m = \frac{- 13 - 6}{- 2 - - 6}$

$m = \frac{- 19}{- 2 + 6}$

$m = \frac{- 19}{4}$

$m = - \frac{19}{4}$

The slope of a line perpendicular to a given line is the negative inverse of the slope of the given line.

So, if the slope of a given line is:

$m$,

the slope of a perpendicular line is:

$- \frac{1}{m}$

For our problem, the slope of the given line is:

$- \frac{19}{4}$

Therefore, the slope of a perpendicular line is:

$- 1 \times - \frac{4}{19}$

$\frac{4}{19}$