Question

What is the slope of any line perpendicular to the line passing through `(-20,32)` and `(-18,40)`?

Answer 1

First of all, find the slope of the line passing through your indicated points.

Explanation:

m = `(y_2 - y_1)/(x_2 - x_1)`

m = `(40 - 32)/ (-18 - (-20))`

m = `8/2`

m = 4

The slope of the original line is 4. The slope of any perpendicular line is the negative reciprocal of the original slope. That's to say that you multiply by -1 and flip the numerator and denominator place's, so that the numerator becomes the new denominator and vice versa.

So, 4 --> `-1/4`

The slope of any line perpendicular to the line passing through (-20,32) and (-18,40) is `-1/4`.

Below I have included a few exercises for your practice.

1. Find the slope of the line perpendicular to the following lines.

a) y = 2x - 6

b) graph{y = 3x + 4 [-8.89, 8.89, -4.444, 4.445]}

c) Passes through the points (9,7) and (-2,6)

1. Are the following systems of equations parallel, perpendicular or neither to each other?

a) 2x + 3y = 6
3x + 2y = 6

b) 4x + 2y = -8
3x - 6y = -12

Enjoy, and most of all, good luck in your futur mathematical endeavours!