number of trees Number of apples

Question

2 26
3 39
6 78
10 130
12 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.

(1 point)
Responses

No, the ratios are not equivalent.
No, the ratios are not equivalent.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

No, the ratio 6 : 78 is not proportional to the other ratios.
No, the ratio 6 : 78 is not proportional to the other ratios.

No, the table does not count consecutively.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to examine the ratios of the number of apples to the number of trees.

1. For 2 trees:
   \( \frac{26}{2} = 13 \)

2. For 3 trees:
   \( \frac{39}{3} = 13 \)

3. For 6 trees:
   \( \frac{78}{6} = 13 \)

4. For 10 trees:
   \( \frac{130}{10} = 13 \)

5. For 12 trees:
   \( \frac{156}{12} = 13 \)

It shows that all the ratios are equal to 13, which indicates a constant ratio.

Based on this evaluation, the correct response is:

Yes, the data table has a proportional relationship.