Question

What is the slope of any line perpendicular to the line passing through `(-15,2)` and `(-10,4)`?

Answer 1

The slope of the perpendicular line is `-5/2`

Explanation:

First, we need to determine the slope of the line going through the two points given in the problem.

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 two points from the problem gives:

`m = (color(red)(4) - color(blue)(2))/(color(red)(-10) - color(blue)(-15))`

`m = (color(red)(4) - color(blue)(2))/(color(red)(-10) + color(blue)(15))`

`m = (2)/(5)`

The slope of a perpendicular line is the negative inverse, so we "flip" the slope and take its negative:

`m_p = -5/2`