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

##### 1 Answer

In general, if the slope of a line is

To see that, consider a line given by

If you reflect that line in the line

If you then reflect that line in the

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

Subtract

Divide both sides by

Notice the new slope is