# What is the slope of any line perpendicular to the line passing through (5,-9) and (-4,-3)?

Jan 6, 2016

$\frac{3}{2}$

#### Explanation:

Let the slope of this line be $m$ and that of the line perpendicular to it be $m '$, then $m . m ' = - 1$

$\implies m ' = - \frac{1}{m} = - \frac{1}{\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} = - \frac{{x}_{2} - {x}_{1}}{{y}_{2} - {y}_{1}} = - \frac{- 4 - 5}{- 3 - \left(- 9\right)} = - \frac{- 9}{- 3 + 9} = - \frac{- 9}{6} = \frac{3}{2}$
$\implies m ' = \frac{3}{2} =$.

$\implies$ the slope of line perpendicular to the line passing through the given points is $\frac{3}{2}$.