Question

On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0).
What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)?

3x + 5y = −9
3x + 5y = 9
5x − 3y = −15
5x − 3y = 15

Answer 1

Slope of the given line = (-1 − 2)/(2 − (−3)) = −3/5, so perpendicular slope = 5/3.

Point-slope through (3,0): y − 0 = (5/3)(x − 3) → 3y = 5x − 15 → 5x − 3y = 15.

Answer: 5x − 3y = 15.