A line passes through (2, 5) with slope 3/4. What is the slope of a line perpendicular to it?

Perpendicular lines have slopes that are negative reciprocals: their product is $-1$. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$, and changing the sign gives $-\frac{4}{3}$, choice C. Check: $\frac{3}{4}\cdot\left(-\frac{4}{3}\right)=-1$. Choice A ($\frac{3}{4}$) is the slope of a parallel line. Choice B ($\frac{4}{3}$) flips the fraction but forgets to change the sign. Choice D ($-\frac{3}{4}$) changes the sign but forgets to flip the fraction. The point $(2,5)$ is given but is not needed to find a perpendicular slope.