# If the slope of a line is 17/13, what is the slope of a perpendicular line?

##### 1 Answer

#### Explanation:

Suppose a line has equation

This is in slope intercept form with slope

If we reflect this line in the line

#x = my + c#

If we then reflect that line in the

#x = -my + c#

Subtract

#x - c = -my#

Divide both sides by

#y = -1/m x + c/m#

This is in slope intercept format.

Notice that the geometric result of the two reflections is a rotation through a right angle (Try it yourself with a square of paper with an arrow on one side).

Notice that the effect on the slope is to replace

Any parallel line will just have a different intercept value, so we have shown that a line perpendicular to a line of slope