Question

What is the slope of any line perpendicular to the line passing through `(-8,23)` and `(5,21)`?

Answer 1

See a solution process below:

Explanation:

The formula for find the slope of a line 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_2), color(red)(y_2))` are two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(21) - color(blue)(23))/(color(red)(5) - color(blue)(-8)) = (color(red)(21) - color(blue)(23))/(color(red)(5) + color(blue)(8)) = -2/13`

Let's call the slope of a perpendicular line: `color(blue)(m_p)`

The slope of a line perpendicular to a line with slope `color(red)(m)` is the negative inverse, or:

`color(blue)(m_p) = -1/color(red)(m)`

Substituting the slope for the line in the problem gives:

`color(blue)(m_p) = (-1)/color(red)(-2/13)= 1/color(red)(2/13) = 13/2`