# What is the slope of a line that is perpendicular to a slope of 1/3?

Mar 23, 2018

-3

#### Explanation:

Perpendicular slopes are opposite reciprocals of each other.

Opposites: positive vs negative

The perpendicular slope of a positive slope must be negative, and vice versa.

Reciprocals: multiplicative inverses (the numbers will multiply to 1)

Examples of reciprocals:

$2 , \frac{1}{2} \rightarrow$ $2 \cdot \frac{1}{2} = 1$

$\frac{1}{3} , 3 \rightarrow$ $\frac{1}{3} \cdot 3 = 1$

The opposite of $\frac{1}{3}$ is $- \frac{1}{3}$, the reciprocal of $- \frac{1}{3}$ is $- 3$.

Mar 23, 2018

$- 3$

#### Explanation:

The slope of two perpendicular lines are negative reciprocals of each other. That means that you flip the fraction upside down and take the opposite of it. The reciprocal of $\frac{1}{3}$ is $3$. The opposite of $3$ is $- 3$. So the slope is $- 3$.