# What is the slope of any line perpendicular to the line passing through (-4,8) and (2,-7)?

May 19, 2016

$\frac{6}{15}$

#### Explanation:

The rule of perpendicular lines is that the product of the slopes of perpendicular lines must be $- 1$. In other words, they are opposite reciprocals of each other.

First, you want to find the slope of this line:
$\frac{- 7 - 8}{2 - - 4} = \frac{- 7 - 8}{2 + 4} = - \frac{15}{6}$

Since the slope of this line is $- \frac{15}{6}$, to get the perpendicular line, we take the reciprocal of this slope:
$- \frac{6}{15}$

Then, we change the sign from a negative to a positive sign:
$\frac{6}{15}$