Question

On a coordinate plane, a line goes through (negative 8, 10), (0, 0), and (8, negative 10).
What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)?

4x – 5y = 5
5x + 4y = 37
4x + 5y = 5
5x – 4y = 8

Answer 1

First line slope = (0 − 10)/(0 − (−8)) = −10/8 = −5/4.
Perpendicular slope = 4/5. Equation through (5,3): y − 3 = (4/5)(x − 5). Multiply out: 5y −15 = 4x −20 → 4x −5y = 5.

Answer: 4x – 5y = 5.