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, 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.

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

Yes, this data table has a proportional relationship

1 answer

To determine if the quantities in the table are in a proportional relationship, we can look at the ratios of miles traveled to hours biked. For a relationship to be proportional, the ratio between the two quantities should remain constant.

Let's calculate 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 compare the ratios:

  • 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 constant (12, 13, 10, 12), the relationship is not proportional.

The correct answer is:
No, not all of the ratios are proportional or have equivalence.