# What is the slope of any line perpendicular to the line passing through (7,-9) and (-5,-3)?

Apr 17, 2018

$2$
$y = 2 x - 23$

#### Explanation:

If by slope you mean gradient, then first work out the gradient of the line that goes through those points:

$\text{change in y"/"change in x" = "gradient}$

$\frac{\left(- 9\right) - \left(- 3\right)}{7 - \left(- 5\right)} = \frac{- 6}{12} = - 0.5$ (as $\left(- -\right) = +$)

The perpendicular gradient will be the negative reciprocal (meaning when multiplied together it produces $- 1$). This is also known as the 'normal'.

Normal of $- 0.5 = 2$

Therefore, gradient is $2$ of the perpendicular line to the line which passes through those 2 points.

If you want the equation of one of those lines then:

$y - \left(- 9\right) = 2 \text{ x } \left(x - 7\right)$
$y + 9 = 2 x - 14$

$y = 2 x - 23$