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