1. **State the problem:** We need to determine which tables represent a proportional relationship between $x$ and $y$. 2. **Recall the rule for proportional relationships:** Two variables $x$ and $y$ are proportional if the ratio $\frac{y}{x}$ is constant for all pairs. 3. **Check each table:** - Table A: Calculate $\frac{y}{x}$ for each pair: $$\frac{5}{2} = 2.5, \quad \frac{10}{4} = 2.5, \quad \frac{15}{6} = 2.5, \quad \frac{20}{8} = 2.5, \quad \frac{25}{10} = 2.5$$ All ratios are equal, so Table A is proportional. - Table B: $$\frac{12}{3} = 4, \quad \frac{20}{5} = 4, \quad \frac{28}{7} = 4, \quad \frac{36}{9} = 4, \quad \frac{44}{11} = 4$$ All ratios equal 4, so Table B is proportional. - Table C: $$\frac{10}{4} = 2.5, \quad \frac{16}{6} \approx 2.67, \quad \frac{24}{8} = 3, \quad \frac{34}{10} = 3.4, \quad \frac{46}{12} \approx 3.83$$ Ratios are not constant, so Table C is not proportional. - Table D: $$\frac{3}{21} = \frac{1}{7} \approx 0.1429, \quad \frac{5}{35} = \frac{1}{7} \approx 0.1429, \quad \frac{7}{49} = \frac{1}{7} \approx 0.1429, \quad \frac{9}{63} = \frac{1}{7} \approx 0.1429, \quad \frac{11}{77} = \frac{1}{7} \approx 0.1429$$ All ratios equal $\frac{1}{7}$, so Table D is proportional. - Table E: $$\frac{7}{6} \approx 1.167, \quad \frac{11}{8} = 1.375, \quad \frac{19}{10} = 1.9, \quad \frac{31}{12} \approx 2.58, \quad \frac{47}{14} \approx 3.36$$ Ratios are not constant, so Table E is not proportional. **Final answer:** Tables A, B, and D represent proportional relationships.