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, 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.

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

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 ratio of miles traveled to hours biked is constant.

Let's calculate the ratios for each row:

1. For 1 hour:
\[
\text{Ratio} = \frac{12 \text{ miles}}{1 \text{ hour}} = 12
\]

2. For 2 hours:
\[
\text{Ratio} = \frac{26 \text{ miles}}{2 \text{ hours}} = 13
\]

3. For 3 hours:
\[
\text{Ratio} = \frac{30 \text{ miles}}{3 \text{ hours}} = 10
\]

4. For 4 hours:
\[
\text{Ratio} = \frac{48 \text{ miles}}{4 \text{ hours}} = 12
\]

Now we can observe the ratios:
- 1 hour: 12
- 2 hours: 13
- 3 hours: 10
- 4 hours: 12

Since these ratios are not all equal, the quantities in the data table do not have a proportional relationship.

Therefore, the correct response is:

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