# What is the slope of any line perpendicular to the line passing through (6,-4) and (3,-13)?

May 22, 2017

The slope of perpendicular line is $- 3$

#### Explanation:

The slope of the line passing through $\left(6 , - 4\right) \mathmr{and} \left(3 , - 13\right)$ is ${m}_{1} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 13 + 4}{3 - 6} = \frac{- 9}{-} 3 = 3$

The product of slopes of two perpendicular lies is ${m}_{1} \cdot {m}_{2} = - 1$

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

The slope of perpendicular line is $- 3$ [Ans]