# What is the slope of any line perpendicular to the line passing through (52,-5) and (31,7)?

Jun 20, 2018

The perpendicular slope is $\frac{21}{12}$.

#### Explanation:

First, find the slope of the line passing through those points.

To find the slope of a line passing through given points, we find the $\text{change in y"/"change in x}$, or $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

We have the points $\left(52 , - 5\right)$ and $\left(31 , 7\right)$

Let's plug it into the formula:
$\frac{7 - \left(- 5\right)}{31 - 52}$

Simplify:
$\frac{7 + 5}{- 21}$

$= \frac{12}{-} 21$

$= - \frac{12}{21}$

To find the slope of the line perpendicular to this line, we find the negative reciprocal, which in this case, is the same thing as making it positive and swapping the numerator and denominator:
$\frac{21}{12}$.

Therefore, the perpendicular slope is $\frac{21}{12}$.

Hope this helps!