To determine if the quantities in the table represent a proportional relationship, we need to check if the ratio of water used to time is constant for all given values.
- Calculate the ratios for each time:
- For 1 minute: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
- For 2 minutes: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
- For 3 minutes: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
- For 7 minutes: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
- For 10 minutes: \( \frac{50 \text{ gal}}{10 \text{ min}} = 5 \)
Since all the ratios simplify to the same value (5), they are indeed equivalent. Therefore, the data table does represent a proportional relationship.
The correct answer is: Yes, the data table has a proportional relationship.