Question

What is the slope of any line perpendicular to the line passing through `(-6,6)` and `(-2,-13)`?

Answer 1

The slope of any perpendicular line will be: `4/19`

Explanation:

First, we need to determine the slope of the line for the two given points.

The slope can be found by using the formula: `color(red)(m = (y_2 = y_1)/(x_2 - x_1)`
Where `m` is the slope and `(x_1, y_1)` and `(x_2, y_2)` are the two points.

Substituting the points provided gives:

`m = (-13 - 6)/(-2 - - 6)`

`m = (-19)/(-2 + 6)`

`m = (-19)/(4)`

`m = -19/4`

The slope of a line perpendicular to a given line is the negative inverse of the slope of the given line.

So, if the slope of a given line is:

`m`,

the slope of a perpendicular line is:

`-1/m`

For our problem, the slope of the given line is:

`-19/4`

Therefore, the slope of a perpendicular line is:

`-1 xx -4/19`

`4/19`