Why perpendicular slope is negative reciprocal

Transcript

Say you have the line y  =mx. So that the slope is m.   Now you want to get the perpendicular  line by rotating 90 degrees this way,   so that x becomes y and y becomes -x. That means 

this y is replaced by -x and this x is replaced   by y. Now let's solve for y by dividing by m both  sides, and then you get y equals to negative (1   over m) x where now negative 1 over m is the  slope of this line that is rotated 90 degrees