# What is the slope of any line perpendicular to the line passing through (-13,9) and (-4,12)?

Apr 5, 2018

The slope of any line pependicular to the line passing
through
$\left(- 13 , 9\right) \mathmr{and} \left(- 4 , 12\right)$ is $- 3$

#### Explanation:

The slope of the line passing through $\left(- 13 , 9\right) \mathmr{and} \left(- 4 , 12\right)$ is

${m}_{1} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{12 - 9}{- 4 + 13} = \frac{3}{9} = \frac{1}{3}$

The product of slopes of the pependicular lines is ${m}_{1} \cdot {m}_{2} = - 1$

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

Therefore ,the slope of any line pependicular to the line passing

through $\left(- 13 , 9\right) \mathmr{and} \left(- 4 , 12\right)$ is $- 3$ [Ans]