Question

What is the slope of any line perpendicular to the line passing through `(-2,8)` and `(0,4)`?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line passing 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)(4) - color(blue)(8))/(color(red)(0) - color(blue)(-2)) = (color(red)(4) - color(blue)(8))/(color(red)(0) + color(blue)(2)) = -4/2 = -2`

Now, let's call the perpendicular slope `m_p`. The formula for the perpendicular slope is:

`m_p = -1/m`

Substituting the slope we calculated for `m` gives:

`m_p = (-1)/(-2)`

`m_p = 1/2`