# What is the slope of any line perpendicular to the line passing through (-5,1) and (11,-4)?

Jan 30, 2016

A line $b$ perpendicular to another line $a$ has a gradient of ${m}_{b} = - \frac{1}{m} _ a$ where ${m}_{a}$ is the gradient (slope) of line $a$. In this case the slope is $\frac{16}{5}$.

#### Explanation:

To find the gradient (slope) of the given line through the points $\left(- 5 , 1\right)$ and $\left(11 , - 4\right)$ use the formula:

$m = \frac{{y}_{2} - {y}_{2}}{{x}_{2} - {x}_{1}} = \frac{- 4 - 1}{11 - \left(- 5\right)} = - \frac{5}{16}$

Lines parallel to this line will have the same slope, lines perpendicular to it will have slope $- \frac{1}{m}$.

In this case, that means the slope of any perpendicular line will be $\frac{16}{5}$.