# What is the slope of any line perpendicular to the line passing through (2,2) and (3,-5)?

Mar 12, 2018

$\frac{1}{7}$

#### Explanation:

Denoting

$\left(2 , 2\right)$ by $\left({x}_{1} , {y}_{1}\right)$

and

$\left(3 , - 5\right)$ by $\left({x}_{2} , {y}_{2}\right)$

The slope of the line is the rise (difference between $y$ values) divided by the run (difference between $x$ values).

Denoting the slope by $m$

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

$= \frac{- 5 - 2}{3 - 2}$

$= - \frac{7}{1}$

that is

$m = - 7$

The slope of a line perpendicular to some other line is the negative reciprocal.

Denoting the required slope by $m '$

$m ' = - \frac{1}{m} = - \frac{1}{- 7} = \frac{1}{7}$