To determine if the quantities in the data table represent a proportional relationship, we need to check if the ratios of water used to time remain constant throughout the data points.
The ratios can be calculated as follows:
- 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 calculated ratios (5) are equivalent, the quantities in the data table do indeed have a proportional relationship.
Therefore, the correct answer is:
Yes, the data table has a proportional relationship.