Question

What is the slope of any line perpendicular to the line passing through `(-5,1)` and `(-14,-4)`?

Answer 1

See a solution process below:

Explanation:

First, we need to find the slope of the line containing 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)(-4) - color(blue)(1))/(color(red)(-14) - color(blue)(-5)) = (color(red)(-4) - color(blue)(1))/(color(red)(-14) + color(blue)(5)) = (-5)/-9 = 5/9`

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

The slope of a perpendicular line is:

`m_p = -1/m`

Substituting gives:

`m_p = -1/(5/9) = -9/5`