1. **State the problem:** We are given a table representing a linear function with points $(4,9)$, $(6,14)$, $(8,19)$, and $(10,24)$. We need to find which given relationship has the same rate of change (slope) as this function. 2. **Find the slope of the given function:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope using points $(4,9)$ and $(6,14)$:** $$m = \frac{14 - 9}{6 - 4} = \frac{5}{2} = 2.5$$ 4. **Check the slope of each given option:** - Option B: $$y = \frac{3}{2}x - 3$$ has slope $\frac{3}{2} = 1.5$ - Option D: $$y = -\frac{7}{4}x - 4$$ has slope $-\frac{7}{4} = -1.75$ 5. **Compare slopes:** The slope of the given function is $2.5$. Neither option B nor D matches this slope. 6. **Analyze graphs A and C:** - Graph A passes through approximately $(2,4)$ and $(5,0)$, slope $$m = \frac{0 - 4}{5 - 2} = \frac{-4}{3} = -1.33$$ - Graph C passes through approximately $(0,-5)$ and $(3,4)$, slope $$m = \frac{4 - (-5)}{3 - 0} = \frac{9}{3} = 3$$ 7. **Compare all slopes:** - Given function slope: $2.5$ - Graph A slope: $-1.33$ - Graph B slope: $1.5$ - Graph C slope: $3$ - Graph D slope: $-1.75$ 8. **Conclusion:** None of the options exactly match $2.5$, but the closest is graph C with slope $3$. Since the problem asks for the same rate of change, none exactly match, but graph C is closest and has an increasing slope like the given function. **Final answer:** The function with the same rate of change is closest to **Graph C**.