# What is the slope of any line perpendicular to the line passing through (-2,17) and (2,8)?

Sep 8, 2016

${m}_{1} = - \frac{9}{4} \text{ " rarr " } {m}_{2} = \frac{4}{9}$

#### Explanation:

If you have 2 points you can find the slope of the line joining them from the formula:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{17 - 8}{- 2 - 2} = \frac{9}{-} 4$

Perpendicular lines have the following properties:

They intersect at 90°
Their slopes are exactly opposite ...
Where one is steep, the other is gentle.
If one is positive, the other is negative.

One slope is the negative reciprocal of the other.

If ${m}_{1} = \frac{a}{b} , \text{ then } {m}_{2} = - \frac{b}{a}$

The product of their slopes is -1

${m}_{1} \times {m}_{2} = - 1$

So in this case:

${m}_{1} = - \frac{9}{4} \text{ " rarr " } {m}_{2} = \frac{4}{9}$