# What is the slope of a line perpendicular to 2y=-6x-10?

Sep 28, 2014

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

Let's begin by putting the current equation in standard form.

$2 y = - 6 x - 10$

$6 x + 2 y = - 10$

The slope of this line is $- \left(\frac{A}{B}\right) = - \left(\frac{6}{2}\right) = - \left(3\right) = - 3$

The negative reciprocal is $- \frac{1}{m} = - \left(\frac{1}{- 3}\right) = \frac{1}{3}$