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 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 ratios are not equivalent.
No, the ratios are not equivalent.
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Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of the number of apples to the number of trees are equivalent for all entries.

We can calculate the ratios for each entry:

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: \( \frac{156}{12} = 13 \)

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

Thus, the correct response is:

Yes, the data table has a proportional relationship.