Question

What is the slope of any line perpendicular to the line passing through `(-2,6)` and `(9,-13)`?

Answer 1

The slope of a perpendicular line is `11/19`

Explanation:

First, we need to determine the slope of the line passing through these two points. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(-13) - color(blue)(6))/(color(red)(9) - color(blue)(-2))`

`m = (color(red)(-13) - color(blue)(6))/(color(red)(9) + color(blue)(2))`

`m = -19/11`

The slope of a perpendicular line, let's call it `m_p` is the negative inverse of the slope of the line it is perpendicular to. Or `m_p = =1/m`

Therefore the slope of a perpendicular line in this problem is:

`m_p = - -11/19`

`m_p = 11/19`