Question

What is the slope of any line perpendicular to the line passing through `(-2,5)` and `(-3,1)`?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line going through 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)(5))/(color(red)(-3) - color(blue)(-2)) = (color(red)(1) - color(blue)(5))/(color(red)(-3) + color(blue)(2)) = (-4)/-1 = 4`

Now, 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)(4) = -1/4`