Question

Find the equation of the line that contains the point (4, 5) and is perpendicular to the line y = (5/4)x − 3.

Answer 1

The product of the slopes of the perpendicular lines must equal -1. Let the unknown slope be m.
(5/4)m = -1
m = -(4/5)
The required equation is of the form:
y = -(4/5)x + b
Plugging in the coordinates of the given point, we get:
5 = -(16/5) + b
b = 8 1/5.
The required equation is therefore:
y = -(4/5)x + 8 1/5