problem: Line $j$ is perpendicular to $\frac{y}{3}+\frac{2x}{5}=2$. What is the slope of line $j$?
solution: First, we find the slope of $\frac{y}{3}+\frac{2x}{5}=2$. We change the form to slope-intercept form. Multiplying both sides by 3, we get $y+\frac{6x}{5}=6$. Moving the $x$ to the right, we get $y=-\frac{6x}{5}+6$. The slopes of two perpendicular lines are negative reciprocals. Therefore, the slope of line $j$ is the opposite reciprocal of $-\frac{6}{5}$ which is $\boxed{\frac56}$.