A line $\ell$ has equation $y = 2x + 5$. Which of the following lines is **perpendicular** to $\ell$?

Two lines are perpendicular if and only if their slopes are **negative reciprocals**. The slope of $\ell$ is $2$, so the perpendicular slope is $-\dfrac{1}{2}$. - **A** ($y = 2x - 5$) has the **same** slope as $\ell$ — that makes the two lines **parallel**, not perpendicular. - **B** ($y = -2x + 9$) negates the slope but does not take the reciprocal. ("Negative" and "negative reciprocal" are different operations.) - **D** ($y = \dfrac{1}{2}x + 5$) is the reciprocal *without* the negative sign. Together with **A** and **B** this is the canonical trio of slope-of-perpendicular traps. Only **C** has slope $-\dfrac{1}{2}$, the negative reciprocal of $2$.