Question

What is the slope of a line parallel and perpendicular to the line going through: `(-7, -3)` and `(6, 8)`?

Answer 1

See the entire solution process below:

Explanation:

First, find the slope of the line going through the two points. 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)(8) - color(blue)(-3))/(color(red)(6) - color(blue)(-7)) = (color(red)(8) + color(blue)(3))/(color(red)(6) + color(blue)(7)) = 11/13`

A line parallel to this line will have the same slope as this line. Therefore, the slope of a parallel line will be: `m = 11/13`

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

`m_p = -1/m`

Therefore, the slope of a perpendicular line is: `m_p = -13/11`