Question

Use the table to answer the question.

Amount of Water Used Over Different Time Intervals
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.

(1 point)
Responses

No, the ratios are not equivalent.
No, the ratios are not equivalent.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

No, the table does not count consecutively.
No, the table does not count consecutively.

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

Answer 1

To determine whether the quantities in the table are in a proportional relationship, we can check if the ratios of the water used to the time intervals are equivalent.

The ratios from the table are as follows:

- 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 ratios (5 for each case) are equivalent, the data does have a proportional relationship.

The correct response is:

**Yes, the data table has a proportional relationship.**