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.
We can quickly see that we can get a solution to the equation if the first fraction is 1 and the second is -1 which gives $(x, y) = (2, -3)$.  Similarly if we let $(x, y) = (-2, 3)$ we get the first fraction to be $-1$ and the second to be 1.  The slope of the line through these two points is $\frac{-3 - 3}{2 - (-2)} = \boxed{- \frac 32}$.
-\frac{3}{2}
Level 4
Algebra
Problem: 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.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the slope of the line determined by the solutions to the equation $\frac{2}{x}+\frac{3}{y} = 0$, we first rearrange the equation to express $y$ in terms of $x$. 

Starting with the original equation, we isolate $\frac{3}{y}$:

$\frac{3}{y} = -\frac{2}{x}$.

Next, we take the reciprocal of both sides to express $y$:

$y = -\frac{3x}{2}$.

This equation is now in the slope-intercept form $y = mx + b$, where $m$ represents the slope. Here, the coefficient of $x$ is $-\frac{3}{2}$, which indicates the slope of the line.

Thus, the slope of the line determined by any two solutions to the equation is $-\frac{3}{2}$.<|END_OF_LATENT|> The final answer is $-\frac{3}{2}$.