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. (1 point) Responses No, the ratios are not equivalent. No, the ratios are not equivalent. No, the table does not count consecutively. No, the table does not count consecutively. Yes, the data table has a proportional relationship. Yes, the data table has a proportional relationship. No, the ratio 7:35 is not proportional to the other ratios.

Answer 1

To determine if the quantities in the data table represent a proportional relationship, we can check the ratios of water used to time for each entry:

1. For 1 min: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
2. For 2 min: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
3. For 3 min: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
4. For 7 min: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
5. For 10 min: \( \frac{50 \text{ gal}}{10 \text{ min}} = 5 \)

Since all the ratios are equal to 5, the quantities in the table do represent a proportional relationship.

Therefore, the correct response is:

Yes, the data table has a proportional relationship.