Question

Question

Use the table to answer the question.

Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.

(1 point)
Responses

No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.

No, none of the ratios have equivalence.
No, none of the ratios have equivalence.

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

No, not all of the ratios are proportional or have equivalence.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to examine the ratios of miles traveled to hours biked.

1. For 1 hour: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \)
2. For 2 hours: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \)
3. For 3 hours: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \)
4. For 4 hours: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \)

Now, we can compare these ratios:

• \( 12, 13, 10, 12 \)

Since the ratios are not all the same, the relationship is not proportional.

Thus, the correct response is:

No, not all of the ratios are proportional or have equivalence.