# What is the slope of any line perpendicular to the line passing through (4,-7) and (1,-12)?

Jan 9, 2016

$- \frac{3}{5}$

#### Explanation:

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

$m = \frac{- 12 - \left(- 7\right)}{1 - 4} = \frac{- 12 + 7}{-} 3 = \frac{- 5}{-} 3 = \frac{5}{3}$

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

Then $m \cdot m ' = - 1 \implies m ' = - \frac{1}{m} = - \frac{1}{\frac{5}{3}} = - \frac{3}{5}$

$\implies m ' = - \frac{3}{5}$

Hence, the slope of the required line is $- \frac{3}{5}$.