Question

What is the slope of the line determined by any two solutions to the equation $\frac{2}{x}+\frac{3}{y} = 0$? Express your answer as a common fraction.

Answer 1

Start with 2/x + 3/y = 0. Multiply by xy (x,y ≠ 0) to get 2y + 3x = 0, so y = (-3/2)x. Thus all solution points lie on a line through the origin with slope -3/2.