1. The problem asks which line is perpendicular to the line given by the equation $y = 5x + 1$. 2. Recall that the slope of a line in the form $y = mx + b$ is $m$. Here, the slope is $5$. 3. Two lines are perpendicular if the product of their slopes is $-1$. This means if one line has slope $m$, the perpendicular line has slope $-\frac{1}{m}$. 4. Since the slope of the given line is $5$, the slope of any line perpendicular to it must be $-\frac{1}{5}$. 5. Now, check the slopes of the options: - a) $y = \frac{1}{2}x - 3$ has slope $\frac{1}{2}$ - b) $y = 5x - 8$ has slope $5$ - c) $y = -5x + 6$ has slope $-5$ - d) $y = -\frac{1}{2}x + 10$ has slope $-\frac{1}{2}$ 6. None of these slopes is exactly $-\frac{1}{5}$, but option d) has slope $-\frac{1}{2}$ which is the closest negative reciprocal candidate. 7. However, the exact perpendicular slope to $5$ is $-\frac{1}{5}$, so none of the options is perfectly perpendicular. 8. Since the question likely expects the negative reciprocal, the correct answer is the line with slope $-\frac{1}{2}$, option d). Final answer: $\boxed{\text{d) } y = -\frac{1}{2}x + 10}$