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The task here is to determine which tables show a proportional relationship between \( x \) and \( y \). A proportional relationship exists when the ratio \( \frac{y}{x} \) is constant for all pairs of values in the table.

### Let's check both tables:

#### First Table (on the left):
- For \( x = 1 \), \( y = \frac{3}{5} \), so \( \frac{y}{x} = \frac{3}{5} \).
- For \( x = 4 \), \( y = \frac{12}{5} \), so \( \frac{y}{x} = \frac{12/5}{4} = \frac{3}{5} \).
- For \( x = 10 \), \( y = 6 \), so \( \frac{y}{x} = \frac{6}{10} = \frac{3}{5} \).

Since the ratio \( \frac{y}{x} = \frac{3}{5} \) is constant across all pairs, this table represents a proportional relationship.

#### Second Table (on the right):
- For \( x = 5 \), \( y = \frac{7}{2} \), so \( \frac{y}{x} = \frac{7/2}{5} = \frac{7}{10} \).
- For \( x = 10 \), \( y = 6 \), so \( \frac{y}{x} = \frac{6}{10} = \frac{3}{5} \).
- For \( x = 15 \), \( y = \frac{17}{2} \), so \( \frac{y}{x} = \frac{17/2}{15} = \frac{17}{30} \).

Here, the ratios are \( \frac{7}{10}, \frac{3}{5}, \frac{17}{30} \), which are not equal. Therefore, this table **does not** show a proportional relationship.

### Conclusion:
- The **first table** shows a proportional relationship.
- The **second table** does not.

Would you like more details, or have any questions about proportional relationships?

Here are 5 related questions to explore further:
1. How can you identify proportional relationships in equations?
2. What are some real-life examples of proportional relationships?
3. How do proportional and non-proportional relationships differ?
4. What is the significance of the constant of proportionality?
5. Can graphs help identify proportional relationships?

**Tip:** In a proportional relationship, the graph will always be a straight line passing through the origin.

Select the tables that show a proportional relationship between x and y.

Understand how to identify proportional relationships in tables by checking if the ratio between x and y remains constant. This step-by-step guide helps 7th-grade students analyze tables to find proportionality using fractions and ratios.

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