# What is the slope of a line perpendicular to x-5y=10?

Sep 28, 2014

The slope of the perpendicular line is the negative reciprocal, $- \frac{1}{m}$.

The slope of the original line is $- \left(\frac{A}{B}\right) = - \left(\frac{1}{- 5}\right) = \frac{1}{5}$

The slope of the perpendicular line is ...

$- \frac{1}{m} = - \frac{1}{\frac{1}{5}} = - 1 \cdot \frac{5}{1} = - \frac{5}{1} = - 5.$