Question

What is the slope of any line perpendicular to the line passing through `(-12,14)` and `(-1,1)`?

Answer 1

See the solution process below:

Explanation:

First, find the slope of the line defined by the two points 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 values from the points in the problem gives:

`m = (color(red)(1) - color(blue)(14))/(color(red)(-1) - color(blue)(-12)) = (color(red)(1) - color(blue)(14))/(color(red)(-1) + color(blue)(12)) = -13/11`

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

The formula for `m_p` is:

`m_p = -1/m`

Substituting the slope we calculated for `m` and calculating `m_p` gives:

`m_p = (-1)/(-13/11) = 11/13`

The slope of a perpendicular line is `11/13`