Question

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
On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0).

Answer 1

Slope of the given line through (-3,2) and (2,-1) is m = (-1−2)/(2−(−3)) = −3/5.
A perpendicular slope is 5/3. Using point-slope through (3,0): y − 0 = (5/3)(x − 3) → y = (5/3)x − 5.
Multiply by 3: 5x − 3y = 15.