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The table in your image represents the cost of T-shirts based on quantity, and you're asked to determine the correct statement about the data.

### Table Summary:
- 1 T-shirt: $10
- 2 T-shirts: $15
- 3 T-shirts: $20
- 4 T-shirts: $25
- 5 T-shirts: $30
- 6 T-shirts: $35

To check the statements:

1. **Proportional relationship:** A proportional relationship means that the ratio between the number of T-shirts and the cost is constant (i.e., the unit rate or cost per T-shirt should be the same for all data points). 

   - Here, the first T-shirt costs $10, and the price increases by $5 for each additional T-shirt.
   - If it were proportional, each T-shirt would cost the same amount, which isn't the case here because the first T-shirt costs $10, and then the price rises by $5 for each additional T-shirt.
   
   Therefore, this is **not a proportional relationship**.

2. **Rate of change:** The rate of change is consistent at $5 for each additional T-shirt after the first.

Thus, the correct answer is:

- **The data do not represent a proportional relationship, but the rate of change of the data is $5 per shirt.**

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the difference between proportional and non-proportional relationships?
2. How do you calculate the rate of change in a data set?
3. Can a non-proportional relationship still have a constant rate of change?
4. What is a constant of proportionality, and how is it different from the rate of change?
5. If the cost of the first T-shirt was $5, would the relationship then be proportional?

**Tip:** For a relationship to be proportional, the cost must increase at a constant rate starting from 0 (e.g., $0 for 0 T-shirts).

Which statement about the data in the table is true?

Analyze a table showing T-shirt purchases to determine whether the relationship between the number of T-shirts and total cost is proportional. This exercise covers the concepts of proportional relationships, rates of change, and cost analysis, suitable for students in Grades 6-8.

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