1. **State the problem:** We are given a function graphed as a line passing through points (0,6) and (3,0) with slope approximately $-2$. We need to find which of the given options represents a function with a lesser rate of change (slope) than this function. 2. **Find the slope of the graphed function:** The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(0,6)$ and $(3,0)$: $$m=\frac{0 - 6}{3 - 0} = \frac{-6}{3} = -2$$ So the slope of the graphed function is $-2$. 3. **Analyze each option's slope:** - Option A: Points $(4,8)$ and $(8,14)$ $$m=\frac{14 - 8}{8 - 4} = \frac{6}{4} = 1.5$$ - Option B: Equation $y = -6x - 2$ has slope $-6$. - Option C: Points $(3,-8)$ and $(5,-12)$ $$m=\frac{-12 - (-8)}{5 - 3} = \frac{-4}{2} = -2$$ - Option D: Equation $y = 6x - 1$ has slope $6$. 4. **Compare slopes to $-2$:** - Option A slope $1.5$ is greater than $-2$ (since $1.5 > -2$). - Option B slope $-6$ is less than $-2$ (more negative). - Option C slope $-2$ equals the graphed function's slope. - Option D slope $6$ is greater than $-2$. 5. **Interpret "lesser rate of change":** Since the original slope is $-2$, a lesser rate of change means a slope closer to zero or smaller in absolute value but not more negative. Among the options, $1.5$ (Option A) is less steep than $-2$ in absolute value and also less negative. 6. **Conclusion:** Option A represents a function with a lesser rate of change than the graphed function. **Final answer:** Option A.