Question

What is the slope of any line perpendicular to the line passing through `(-6,17)` and `(2,18)`?

Answer 1

`-8`

Explanation:

First, we need to find the slope of the line passing through `(-6,17)` and `(2,18)`. The slope is;

`(18-17)/(2-(-6)) = 1/8`

If we multiply the slope of any line with `-1` and then get its reciprocal, we find the slope of the line which is perpendicular to it.

So;

`1/8.-1=-1/8` its reciprocal `->` `-8`

Answer 2

slope = -8

Explanation:

The first step is to calculate the gradient ( slope) of the line passing through the 2 given points using the `color(blue)" gradient formula "`

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

where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "`

let `(x_1,y_1)=(-6,17)" and " (x_2,y_2)=(2,18)`

`rArr m = (18-17)/(2-(-6)) = 1/8`

If 2 lines with gradients , say `m_1" and " m_2" are perpendicular"`

Then `m_1 xx m_2 = -1`

`rArr 1/8xxm_2 = -1 rArr m_2 =-1/(1/8) = -8`