Question

What is the slope of any line perpendicular to the line passing through `(-20,32)` and `(1,5)`?

Answer 1

`7/9`

Explanation:

Given two lines with slopes `m_1` and `m_2`, we say the lines are perpendicular if `m_1m_2 = -1`. Note that this implies `m_2= -1/m_1`.

Then, to find the slope `m_2` of a line perpendicular to the line passing through `(-20, 32)` and `(1, 5)` all we need to do is find the slope `m_1` of the given line and apply the above formula.

The slope of a line passing through points `(x_1,y_1)` and `(x_2,y_2)` is given by `"slope" = "increase in y"/"increase in x" = (y_2-y_1)/(x_2-x_1)`

So
`m_1 = (5-32)/(1-(-20)) = (-27)/21 = -9/7`

Applying `m_2 = -1/m_1` this means the slope `m_2` of a line perpendicular to that line will be

`m_2 = -1/(-9/7) = 7/9`