Use the table to answer the question.

Question

# of Trees # of Apples
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 table does not count consecutively.
No, the table does not count consecutively.

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

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

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

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we can check if the ratio of the number of apples to the number of trees is the same for all entries.

Let's calculate the ratio of apples to trees for each pair of values:

1. For 2 trees and 26 apples:
   Ratio = 26 / 2 = 13

2. For 3 trees and 39 apples:
   Ratio = 39 / 3 = 13

3. For 6 trees and 78 apples:
   Ratio = 78 / 6 = 13

4. For 10 trees and 130 apples:
   Ratio = 130 / 10 = 13

5. For 12 trees and 156 apples:
   Ratio = 156 / 12 = 13

Since all ratios are equivalent and equal to 13, the quantities in the data table are indeed in a proportional relationship.

Thus, the correct response is:

Yes, the data table has a proportional relationship.