The line L has equation y = 5 - 2x. (a) Show that the point P (3, -1) lies on L. (b) Find an equation of the line perpendicular to L that passes through P.

(a) To confirm that point P lies on L, we must substitute x = 3 into the equation and see if we get y = -1. y = 5 - 2(3) = -1, therefore P lies on the line L (b) The gradient of the perpendicular line is -1/m, where m is the gradient in line L.
Gradient of perpendicular line = -1/-2 = 1/2 We know that the line passes through point P, so using the equation (y - y1) = m(x - x1) we can find the equation of the perpendicular line (y - (-1)) = 1/2(x - 3) Simplifying this we get, 2y + 2 = x - 3 2y - x + 5 = 0