Question

How do you find the slope that is perpendicular to the line (-3,6) (9,7)?

Answer 1

See the entire solution process below:

Explanation:

First, find the slope of this line using the two points from 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 points from the problem gives:

`m = (color(red)(7) - color(blue)(6))/(color(red)(9) - color(blue)(-3))`

`m = (color(red)(7) - color(blue)(6))/(color(red)(9) + color(blue)(3))`

`m = 1/12`

The slope of a perpendicular line will be the negative inverse, or `-1/m` of the given line. Taking the negative inverse of the slope we calculated gives:

`-12/1 = -12`

The slope of a perpendicular line will be `-12`