# What is the slope of a line perpendicular to a line with a slope of 3?

Jul 11, 2018

${m}_{1} = 3$

${m}_{2} = - \frac{1}{3}$

#### Explanation:

If two lines are perpendicular then the product of their slopes is $- 1$.

This means one slope is the negative reciprocal of the other.

$\frac{a}{b} \times - \frac{b}{a} = - 1$

So if one slope is $\frac{3}{1}$, the slope perpendicular would be $- \frac{1}{3}$

$\frac{3}{1} \times - \frac{1}{3} = - 1$

One slope will be positive and one will be negative.

One will be steep and the other will be gentle.