In the $xy$-plane, line $\ell$ passes through the origin and is perpendicular to the line $4x + 3y = 12$. What is the equation of line $\ell$?

Rewrite the given line in slope-intercept form: $3y = -4x + 12 \Rightarrow y = -\tfrac{4}{3}x + 4$. Its slope is $-\tfrac{4}{3}$. A perpendicular line has the **negative reciprocal** slope: $\tfrac{3}{4}$. Line $\ell$ passes through the origin, so its $y$-intercept is $0$: $y = \tfrac{3}{4}x$. - Trap A repeats the original slope. - Trap B flips the sign but doesn't take the reciprocal. - Trap C flips both — over-correcting.