To determine if the quantities in the data table represent a proportional relationship, we check if the ratios of water used to time are equivalent for all entries.
Calculating the ratios:
- For 1 min: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
- For 2 min: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
- For 3 min: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
- For 7 min: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
- For 10 min: \( \frac{50 \text{ gal}}{10 \text{ min}} = 5 \)
Since all the ratios simplify to the same number (5), they are constant and represent a proportional relationship.
Therefore, the correct response is:
Yes, the data table has a proportional relationship.