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To determine which table shows a proportional relationship, we need to check if the ratio between "Hours" and "Earnings" is constant for each table. A proportional relationship exists when the ratio between the two variables is the same for all data points.

### Let's check each option:

1. **Table A**:
   - Hours: 4, 6, 8
   - Earnings: 36, 54, 72
   - Ratios: 
     \[
     \frac{36}{4} = 9, \quad \frac{54}{6} = 9, \quad \frac{72}{8} = 9
     \]
   The ratio is constant (9), so **Table A** is proportional.

2. **Table B**:
   - Hours: 4, 6, 8
   - Earnings: 36, 45, 54
   - Ratios:
     \[
     \frac{36}{4} = 9, \quad \frac{45}{6} = 7.5, \quad \frac{54}{8} = 6.75
     \]
   The ratios are not constant, so **Table B** is **not proportional**.

3. **Table C**:
   - Hours: 2, 3, 4
   - Earnings: 9, 18, 27
   - Ratios:
     \[
     \frac{9}{2} = 4.5, \quad \frac{18}{3} = 6, \quad \frac{27}{4} = 6.75
     \]
   The ratios are not constant, so **Table C** is **not proportional**.

4. **Table D**:
   - Hours: 2, 3, 4
   - Earnings: 18, 27, 54
   - Ratios:
     \[
     \frac{18}{2} = 9, \quad \frac{27}{3} = 9, \quad \frac{54}{4} = 13.5
     \]
   The ratios are not constant, so **Table D** is **not proportional**.

### Conclusion:
**Table A** shows a proportional relationship because it has a constant ratio of 9 between hours and earnings.

Would you like further details or have any questions?

### Follow-up questions:
1. What is a proportional relationship in mathematics?
2. How can you identify a proportional relationship from a graph?
3. Can a proportional relationship have a constant other than 1?
4. How do unit rates help in identifying proportional relationships?
5. Are there cases where the ratio can slightly change but still be considered proportional?

**Tip:** When checking for proportional relationships, always verify that the ratio between the two quantities remains constant across all pairs of values.

Which of these tables shows a proportional relationship?

Learn how to identify proportional relationships using a table of values. This example explores the relationship between hours and earnings by checking if the ratio between the two is constant. Suitable for students in Grades 6-8.

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