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 ratio 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.

No, the table does not count consecutively.
No, the table does not count consecutively.

No, the ratios are not equivalent.

Answer 1

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

Let's calculate the ratios for each pair of values:

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

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

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

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

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

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

Therefore, the correct response is: Yes, the data table has a proportional relationship.