# How do you find the slope perpendicular to (-5,-6), (-4,-1)?

Mar 30, 2018

The slope perpendicular to $\frac{5}{1}$ is $- \frac{1}{5}$.

Refer to the explanation for the process.

#### Explanation:

Find the slope using the following formula:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$,

where $m$ is the slope, $\left({x}_{1} , {y}_{1}\right)$ is one point, and $\left({x}_{2} , {y}_{2}\right)$ is the other point. I'm going to use $\left(- 5 , - 6\right)$ as point 1, and $\left(- 4 , - 1\right)$ as point 2.

Plug in the known values and solve.

$m = \frac{- 1 - \left(- 6\right)}{- 4 - \left(- 5\right)}$

$m = \frac{- 1 + 6}{- 4 + 5}$

$m = \frac{5}{1}$

Find the perpendicular slope.

The slopes of two perpendicular lines when multiplied equal $- 1$.

${m}_{1} \cdot {m}_{2} = - 1$

${m}_{2} = - \frac{1}{m} _ 1$

${m}_{2} = - \frac{1}{\frac{5}{1}}$

${m}_{2} = - 1 \times \frac{1}{5}$

${m}_{2} = - \frac{1}{5}$

The slope perpendicular to $\frac{5}{1}$ is $- \frac{1}{5}$.