Question

Use the table to answer the question.

Number of Miles Walked Corresponding to the Number of Hours Spent Biking
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, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.

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.

Answer 1

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

Let's calculate the ratios for each hour biked:

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

Now, looking at the ratios:

- 1 hour: 12
- 2 hours: 13
- 3 hours: 10
- 4 hours: 12

Since the ratios are not all the same (they vary: 12, 13, 10, 12), the quantities are **not in a proportional relationship**.

Therefore, the correct response is:

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