1. **State the problem:** We need to find which line is parallel to the line given by the equation $y = 4x - 7$. 2. **Recall the rule for parallel lines:** Two lines are parallel if and only if they have the same slope. 3. **Identify the slope of the given line:** The equation is in slope-intercept form $y = mx + b$, where $m$ is the slope. For $y = 4x - 7$, the slope $m = 4$. 4. **Check each option's slope:** - a) $y = 4x + 1$ has slope $4$. - b) $y = \frac{1}{4}x - 3$ has slope $\frac{1}{4}$. - c) $y = -4x + 2$ has slope $-4$. - d) $y = -7x + 4$ has slope $-7$. 5. **Compare slopes:** Only option a) has the same slope $4$ as the original line. **Final answer:** The line parallel to $y = 4x - 7$ is $y = 4x + 1$ (option a).