1. **State the problem:** The cost of apples is directly proportional to the weight of the apples. Carlos bought 10 pounds of apples for a cost of 15. We need to find which graph correctly represents the relationship between weight (pounds) and cost (dollars). 2. **Formula and rules:** For direct proportionality, the relationship is given by: $$\text{Cost} = k \times \text{Weight}$$ where $k$ is the constant of proportionality (cost per pound). 3. **Find the constant $k$:** Given: weight = 10 pounds, cost = 15 $$15 = k \times 10$$ Divide both sides by 10: $$15 = k \times \cancel{10} \\ \Rightarrow \frac{15}{\cancel{10}} = k \\ k = \frac{15}{10} = 1.5$$ 4. **Interpretation:** The cost per pound is $1.5$. So the graph should be a straight line through the origin with slope $1.5$. 5. **Check the graphs:** - Graph A: slope = 1 (cost increases 1 dollar per pound) - Graph B: slope < 1 - Graph C: slope > 1 (approximately 10 dollars at 6 pounds, slope $\approx \frac{10}{6} = 1.67$) - Graph D: slope < 1 Since $k=1.5$, the graph closest to slope 1.5 is Graph C. **Final answer:** Graph C shows the correct relationship.