Question

What is the slope of the line perpendicular to the line passing through the points `( 8, - 2) and (3, - 1)`?

Answer 1

`m=5`

Explanation:

Find the slope of the line joining the two points first.

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

`m = (-1-(-2))/(3-8) = 1/-5`

lines that are perpendicular: the products of their slopes is `-1`.

`m_1 xx m_2 = -1`

One slope is the negative reciprocal of the other.
(This means flip it and change the sign.)

`-1/5 rarr +5/1`

The perpendicular line has a slope of `5`

`-1/5 xx5/1 =-1`

Answer 2

+5

Explanation:

Note that they have deliberately not put the order of the points to match that which you would normally read them. Left to right on the x-axis.

Set left most point as `P_1->(x_1,y_1)=( 3,-1)`
Set right most point as `P_2->(x_2,y_2)=(8,-2)`

Suppose the slope of the given line is `m`. The the slope of the line perpendicular to it is `(-1)xx1/m`

Reading left to right we have:

Slope of given line is:

`("change in y")/("change in x") ->(y_2-y_1)/(x_2-x_1)=((-2)-(-1))/(8-3)=(-1)/5 = m`

The perpendicular line has the slope:

`(-1)xx1/m=(-1)xx(-5/1)=+5`

Answer 3

Slope=5

Explanation:

First, we need to calculate the gradient/slope of the line.

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

I'm going to let `(x_1,y_1)` be `(8,-2)`
and `(x_2,y_2)` be `(3,-1)`

`m=(-1+2)/(3-8)`

`m=1/-5`

There is a rule that states `m_1m_2=-1` which means that if you multiply two gradients together and they equal to `-1`, then they must be perpendicular.

If I let `m_1=-1/5`,
then `-1/5m_2=-1` and `m_2=5`

Therefore, the slope is equal to 5