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To determine which table represents a direct proportion, we need to check if there is a consistent ratio between the values of \( x \) and \( y \) in each table.

A relationship is a direct proportion if \( y = kx \), where \( k \) (the constant of proportionality) remains the same for each pair of \( x \) and \( y \).

### Analyzing Each Table:

1. **Table A**:
   - Ratios: \( \frac{y}{x} = \frac{2}{5}, \frac{4}{10}, \frac{6}{15}, \frac{8}{20} \).
   - All ratios are \( \frac{2}{5} \), which is constant. Therefore, **Table A** shows direct proportion.

2. **Table B**:
   - Ratios: \( \frac{y}{x} = \frac{2}{1}, \frac{5}{2}, \frac{7}{3}, \frac{8}{4} \).
   - Ratios are not consistent. Thus, **Table B** does not represent direct proportion.

3. **Table C**:
   - Ratios: \( \frac{y}{x} = \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8} \).
   - Ratios are not consistent. Thus, **Table C** does not represent direct proportion.

4. **Table D**:
   - Ratios: \( \frac{y}{x} = \frac{4}{2}, \frac{8}{4}, \frac{12}{6}, \frac{16}{8} \).
   - All ratios are \( 2 \), which is constant. Therefore, **Table D** shows direct proportion.

### Conclusion:
Both **Table A** and **Table D** represent direct proportion, but since the question is asking for a single answer, if only one choice can be made, you would generally select **Table A** (as it is likely meant to be the primary answer in multiple-choice settings).

Would you like more details on this analysis or have any questions?

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### Further Questions:
1. What is the constant of proportionality for each table?
2. How can you identify inverse proportion in similar tables?
3. Why does a constant ratio confirm direct proportion?
4. Can we graph these tables to visualize direct proportion?
5. How would the values change if these tables represented inverse proportions?

### Tip:
When checking for direct proportion, calculating the ratio \( \frac{y}{x} \) for each pair helps confirm if it remains constant.

Which of the following tables represents a direct proportion?

Learn how to identify direct proportion from tables by checking for a constant ratio between x and y values. Explore which tables follow the formula y = kx and see how the ratios confirm direct proportionality. This math problem is suitable for students in Grades 6-8.

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