3x + 5y = −9 can be solved for y (and thus for the slope explicitly):
5y = -3x - 9, or y = (-3/5)x - 9/5. The slope of the given line is -3/5. The slope of a line perpendicular to the given line is the negative reciprocal of this -3/5, which is 5/3. Substituting 3 for x and 0 for y, our slope-intercept equation y = mx + b becomes 0 = (5/3)(3) + b, which leads to b = -5:
y = (5/3)x - 5. We must put this back into standard form, starting by multiplying all three terms by 3:
3y = 5x - 15, or -5x + 3y = -15. This is equivalent to 5x - 3y = 15 (which is the last answer choice).
