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To determine which of these tables represents a direct proportion, we need to check if \( y \) is directly proportional to \( x \). In a direct proportion, the ratio \( \frac{y}{x} \) should remain constant across all values in the table.

### Analyzing Each Table

- **Table A**:
  \[
  \frac{y}{x} = \frac{2}{5}, \frac{4}{10}, \frac{6}{15}, \frac{8}{20}
  \]
  Each of these simplifies to \( \frac{2}{5} \), indicating a constant ratio. **Table A** represents a direct proportion.

- **Table B**:
  \[
  \frac{y}{x} = \frac{2}{1}, \frac{5}{2}, \frac{7}{3}, \frac{8}{4}
  \]
  These ratios are not constant, so **Table B** does not represent a direct proportion.

- **Table C**:
  \[
  \frac{y}{x} = \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}
  \]
  These ratios are not constant, so **Table C** does not represent a direct proportion.

- **Table D**:
  \[
  \frac{y}{x} = \frac{4}{2}, \frac{8}{4}, \frac{12}{6}, \frac{16}{8}
  \]
  Each of these simplifies to \( 2 \), indicating a constant ratio. **Table D** also represents a direct proportion.

### Conclusion
Both **Table A** and **Table D** represent direct proportions, as their \( \frac{y}{x} \) ratios remain constant.

Would you like further details, or have any questions?

### Related Questions
1. How can you identify direct variation in other types of tables?
2. What other methods can be used to confirm a direct proportion relationship?
3. How does a direct proportion differ from an inverse proportion?
4. Can a table have a constant difference and still represent direct proportion?
5. What is the significance of proportional relationships in real-world applications?

### Tip
Remember, in direct proportion, the ratio \( \frac{y}{x} \) remains constant across all values.

Which of the following tables represents a direct proportion?

Analyze tables to identify which one represents a direct proportion by checking for a constant y/x ratio. Learn the methods used in identifying direct proportionality, suitable for students in Grades 6-8.

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