# What is the slope of any line perpendicular to the line passing through (-12,14) and (-13,1)?

Jan 11, 2016

$- \frac{1}{13}$

#### Explanation:

Let the slope of the line passing through the given points be $m$.

$m = \frac{1 - 14}{- 13 - \left(- 12\right)} = \frac{- 13}{- 13 + 12} = \frac{- 13}{-} 1 = 13$

Let the slope of the line perpendicular to the line passing through the given points be $m '$.

Then $m \cdot m ' = - 1 \implies m ' = - \frac{1}{m} = - \frac{1}{13}$

$\implies m ' = - \frac{1}{13}$

Hence, the slope of the required line is $- \frac{1}{13}$.