This document discusses calculating the equation of a perpendicular line through a given point. It provides three examples of finding the slope of the perpendicular line using the inverse reciprocal of the original line's slope, then determining the y-intercept by plugging the point into the perpendicular line equation.

1. Equation of a Perpendicular Line Through a given Point by D. Fisher

3. -2 3 slope = rise / run m = - 2 / 3 m = -2 / 3

4. Equation of a Perpendicular Line point ( 14 , 4 ) slope = -2 / 3 X y y = mx + b 4 = 3 / 2 14 + b ┴ m = 3 / 2 4 = 3 / 2 14 + b 1 7 4 = 21 + b y = 3 / 2 x – 17 - 21 - 21 – 17 = b

5. -3 -3 3 3 0 -6 6 -6 6 Y X point = ( -3 , 2 ) slope of line = 1 4 1 4 slope of ┴ line = - 4 1 = - 4 2 = - 4 ( - 3 ) + b -12 -12 y = - 4x - 10 2 = 12 + b -10 = b y = mx + b

6. -3 -3 3 3 0 -6 6 -6 6 Y X point = ( 3 , 4 ) slope of line = -1 2 -1 2 slope of ┴ line = 2 1 = 2 4 = 2 ( 3 ) + b 4 = 6 + b -6 - 6 y = 2x - 2 -2 = b

7. -3 -3 3 3 0 -6 6 -6 6 Y X point = ( 2 , -3 ) slope of line = 2 5 2 5 slope of ┴ line = -5 2 -3 = -5 / 2 ( 2 ) + b 2 = b +5 +5 y = -5 / 2 x + 2 - 3 = - 5 + b