The Perpendicular Slope

Two lines are perpendicular when they meet at a right angle. To find the slope of a perpendicular line, flip the fraction and change the sign. The slope perpendicular to $\frac{2}{3}$ is $\frac{-3}{2}$. The slope perpendicular to 2, which is $\frac{2}{1}$, is $\frac{-1}{2}$. As a rule:

$$m\cdot 2 = \frac{-1}{m}\cdot 1$$

When you multiply two perpendicular slopes, you always get -1. You can use this to check that two lines are at right angles.

Why does the fraction flip? A slope is rise over run. When you turn a line by a quarter turn, the rise becomes the run and the run becomes the rise, and one of them changes sign. A horizontal line has slope 0. The line perpendicular to it is vertical, and a vertical line has no slope.