1. **State the problem:** Find the equation of a line parallel to the line given by $$y = -8x + 8$$ that passes through the point $$(4, -7)$$. 2. **Recall the rule for parallel lines:** Parallel lines have the same slope. The slope of the given line is $$m = -8$$. 3. **Use the point-slope form of a line:** $$y - y_1 = m(x - x_1)$$ where $$(x_1, y_1) = (4, -7)$$ and $$m = -8$$. 4. **Substitute the values:** $$y - (-7) = -8(x - 4)$$ which simplifies to $$y + 7 = -8x + 32$$ 5. **Isolate $$y$$ to get slope-intercept form:** $$y = -8x + 32 - 7$$ $$y = -8x + 25$$ 6. **Final answer:** The equation of the line parallel to $$y = -8x + 8$$ passing through $$(4, -7)$$ is $$y = -8x + 25$$.