Question

Proportional Relationships in Tables Quick Check
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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 constant.

Here are the ratios from the table:

- 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: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \)

The ratios are not constant:
- The ratio for 1 hour is 12.
- The ratio for 2 hours is 13.
- The ratio for 3 hours is 10.
- The ratio for 4 hours is 12.

Since the ratios are not the same, the data does not represent a proportional relationship.

Therefore, the correct response is:

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