What is the slope of any line perpendicular to the line passing through (5,0) and (-4,-3)?

Mar 11, 2018

The slope of a line perpendicular to the line passing through $\left(5 , 0\right)$ and $\left(- 4 , - 3\right)$ will be $- 3$.

Explanation:

The slope of a perpendicular line will be equal to the negative inverse of the slope of the original line.

We have to begin by finding the slope of the original line. We can find this by taking the difference in $y$ divided by the difference in $x$:
$m = \frac{0 - \left(- 3\right)}{5 - \left(- 4\right)} = \frac{3}{9} = \frac{1}{3}$

Now to find the slope of a perpendicular line, we just take the negative inverse of $1 \frac{\setminus}{3}$:

$- \frac{1}{\frac{1}{3}} = - 1 \cdot \frac{3}{1} = - 3$

This means that the slope of a line perpendicular to the original one is $- 3$.