Question

What is the slope of a line perpendicular to `x - 3y = 9`?

Answer 1

Let `r` and `s` be to lines, and `m_r` and `m_s` their slopes. The two lines are perpendicular if the following relation holds:

`m_s = -1/m_r`

So, we must find the slope of the line `x-3y=9`, and using the relation wrote above we'll find the perpendicular slope.

To find the slope of a line, we must manipulate its equation in order to bring it into the form

`y=mx+q`

and once in that form, `m` will be the slope. Starting from `x-3y=9`, we can add `3y` to both sides, obtaining `x=3y+9`. Subtracting `9` from both sides, we get `x-9=3y`. Finally, dividing by `3` both sides, we have `y=1/3 x - 3`.

Since our slope is `1/3`, its perpendicular slope will be `-3`