The function f is defined by f(x) = kx + 5. If the graph of f is perpendicular to the line y = -2x + 3, what is the value of k?

Two lines are perpendicular when the product of their slopes is $-1$ (the slopes are negative reciprocals). The line $y = -2x + 3$ has slope $-2$, and $f$ has slope $k$. So $k \cdot (-2) = -1$, giving $k = \frac{1}{2}$. The intercept 5 does not matter for perpendicularity. Common wrong answers: $-\frac{1}{2}$ takes the reciprocal but forgets to flip the sign, 2 is the opposite of $-2$, and $-2$ would make the lines parallel. Perpendicular means flip the fraction and change the sign.