problem: What is the slope of a line perpendicular to the line whose equation is $\frac{x}4-\frac{y}5=1$? Express your answer as a common fraction.
solution: In slope-intercept form, the given equation becomes $y=\frac{5}{4}x-5$.  The slope of this line is $\frac{5}{4}$, so the slope of a line perpendicular to this one is the negative of the reciprocal of $\frac{5}{4}$, or $\boxed{-\frac{4}{5}}.$