What is the equation of the line that passes through the point (3, -2) and is perpendicular to the line 2x - 3y = 5?

✓ Correct Answer: Option B

The given line 2x - 3y = 5 has a slope of 2/3 (from y = (2/3)x - 5/3). A perpendicular line will have a slope of -3/2. Using the point-slope form y - y1 = m(x - x1): y - (-2) = (-3/2)(x - 3). This simplifies to 2(y + 2) = -3(x - 3), so 2y + 4 = -3x + 9. Rearranging gives 3x + 2y = 5.