Question

What is the slope of any line perpendicular to the line passing through `(-6,1)` and `(-2,5)`?

Answer 1

First we need to determine the slope of the line passing through the two points in the problem. The formula for calculating the slope is:

`m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` and `(color(red)(x_1), color(red)(y_1))` are two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(5) - color(blue)(1))/(color(red)(-2) - color(blue)(-6)) = (color(red)(5) - color(blue)(1))/(color(red)(-2) + color(blue)(6)) = 4/4 = 1`

Let's call the slope of the perpendicular line `m_p`

The rule for calculating the slope of a perpendicular line is:

`m_p = -1/m`

Substituting the slope we calculated gives:

`m_p = -1/1` = -1