Use the table to answer the question.

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

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

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

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

4.No, none of the ratios have equivalence.

Answer 1

To determine if the quantities in the data table represent a proportional relationship, we need to compare the ratios of miles traveled to hours biked for each entry in the table.

Calculating the ratios:

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, let's summarize the ratios:

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

Since the ratios are not constant (they vary for each time period), the quantities do not have a proportional relationship.

Therefore, the correct response is: 3. No, not all of the ratios are proportional or have equivalence.