1. The problem asks to find which relationship represents a function with a lesser slope than the function $y = -2x + 8$. 2. The slope of the given function is $-2$. 3. We need to find the slope of each option and compare it to $-2$. 4. For option A, calculate the slope using two points $(4, -5)$ and $(8, -12)$: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - (-5)}{8 - 4} = \frac{-12 + 5}{4} = \frac{-7}{4} = -1.75$$ 5. For option B, calculate the slope using two points $(3, -13)$ and $(6, -22)$: $$m = \frac{-22 - (-13)}{6 - 3} = \frac{-22 + 13}{3} = \frac{-9}{3} = -3$$ 6. For graph C, the line passes through approximately $(-6, 4)$ and $(6, -8)$: $$m = \frac{-8 - 4}{6 - (-6)} = \frac{-12}{12} = -1$$ 7. For graph D, the line passes through approximately $(-6, -6)$ and $(6, 8)$: $$m = \frac{8 - (-6)}{6 - (-6)} = \frac{14}{12} = \frac{7}{6} \approx 1.17$$ 8. Now compare each slope to $-2$: - Option A slope: $-1.75$ which is greater than $-2$ (less negative). - Option B slope: $-3$ which is less than $-2$ (more negative). - Graph C slope: $-1$ which is greater than $-2$ (less negative). - Graph D slope: $1.17$ which is positive and greater than $-2$. 9. The question asks for a function with a lesser slope than $-2$, meaning slope less than $-2$ (more negative). 10. Only option B has slope $-3$ which is less than $-2$. **Final answer:** Option B represents a function with a lesser slope than $y = -2x + 8$.