Time (min) - Water used (gal)

1 - 5
2 - 10
3 - 15
7 - 35
10 - 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 ratios are not equivalent.

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

No, the table does not count consecutively.

Yes, the data table has a proportional relationship.

1 answer

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:

  1. For 1 minute: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
  2. For 2 minutes: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
  3. For 3 minutes: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
  4. For 7 minutes: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
  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.