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

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

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

Yes, this data table has a proportional relationship.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of miles traveled to hours biked are equivalent. A proportional relationship means that the ratio (miles per hour) remains constant.

Let's calculate the ratios for each entry:

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 summarize the ratios:
- 1 hour: 12 miles (ratio = 12)
- 2 hours: 26 miles (ratio = 13)
- 3 hours: 30 miles (ratio = 10)
- 4 hours: 48 miles (ratio = 12)

Since not all of the ratios are the same (12, 13, 10, and 12), we can conclude that the quantities are **not** in a proportional relationship.

Therefore, the correct response is:

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