1. The problem asks to find which relationship represents a function with a lesser slope than the function $y = -2x - 3$. 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, for example $(4, -5)$ and $(8, -12)$: $$\text{slope} = \frac{-12 - (-5)}{8 - 4} = \frac{-7}{4} = -1.75$$ 5. For option B, calculate the slope using two points, for example $(3, -13)$ and $(6, -22)$: $$\text{slope} = \frac{-22 - (-13)}{6 - 3} = \frac{-9}{3} = -3$$ 6. For Graph C, the line decreases from top left to bottom right, so slope is negative. It crosses y-axis near 6 and x-axis near 3, so slope is: $$\text{slope} = \frac{0 - 6}{3 - 0} = \frac{-6}{3} = -2$$ 7. For Graph D, the line increases from bottom left to top right, so slope is positive, which is greater than $-2$. 8. Compare slopes: - 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 = $-2$ equal to given slope. - Graph D slope is positive, 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 less than $-2$. Final answer: Option B represents a function with a lesser slope than $y = -2x - 3$.