Question

Use the table to answer the question

Time ( min ) 1 2 3 7 10

Water Used ( gal ) 5 10 15 35 50

Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship indicate why

No, the table does not count consecutively

Yes, the data table has a proportional relationship

No, the ratios are not equivalent

No, the ratio 7: 35 is not proportional to other ratios

Answer 1

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.

1. 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.**