# What is the slope of the line perpendicular to  y=1/3x-23 ?

Mar 8, 2018

Using some basic geometry, you can find that the slope would be -3

#### Explanation:

If you treat the slope of the equation as a change in y over change in x, you can treat it like a triangle with sides of 1,3, and $\sqrt{10}$.

The angle that the line makes with a horizontal is ${\tan}^{-} 1 \left(\frac{1}{3}\right)$, which is 18.435 degrees.

Adding 90 degrees to this gives you a perpendicular angle, 108.435.

Take the tangent of 108.435 and you get -3