Question

If a line goes through the points (-2,1) and (3,8) what is the slope of a line that is perpendicular to it?

Answer 1

First, you have to determine the slope of the given line and apply the fact that the product of the slopes of two lines that are perpendicular is negative one.

So let us find the slope of the line connecting (-2,1) and

(3,8)

Recall the formula for finding the slope is

`(y_2 -y_1 )/(x_2 - x_1)`

Now, let the slope this line be m, then

`m=(8 - 1 )/(3 - - 2)`

`\Righarrow m=(8 - 1 )/(3 + 2)`

`\Righarrow m=(7)/(5)`

We now let the slope of the line perpendicular to it be n, then

`m* n = -1`

`\Righarrow (7)/(5) * n = -1`

`n = -1 * (5)/(7)`

Hence the slope of the line perpendicular to it, is

`-(5)/(7)`