Question

How do you find the slope of a line perpendicular to a slope of a line is 1/3?

Answer 1

In general, if the slope of a line is `m`, then the slope of any perpendicular line will be `-1/m`. So in your case the slope of any perpendicular line would be `-1/(1/3) = -3`.

To see that, consider a line given by

`y = mx+c`

If you reflect that line in the line `y=x`, you get a line whose equation is the same, but with `x` and `y` swapped:

`x = my+c`

If you then reflect that line in the `x` axis, you are basically reversing the sign of the `y` coordinate, so you get a line with equation:

`x = -my+c`

The total result of these two geometric operations is to rotate the original line through a right angle (try it yourself with a square of paper).

Now we can rearrange this new line's equation into slope intercept form as follows:

Add `my` to both sides:

`my + x = c`

Subtract `x` from both sides:

`my = -x + c`

Divide both sides by `m`:

`y = (-1/m)x + c/m`

Notice the new slope is `-1/m`.