Question

Use the table to answer the 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

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.

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.

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 check if the ratio of the number of apples to the number of trees remains constant for all entries.

Let's calculate the ratio of apples to trees for each row in the table:

- For 2 trees: 26 apples → Ratio = \( \frac{26}{2} = 13 \)
- For 3 trees: 39 apples → Ratio = \( \frac{39}{3} = 13 \)
- For 6 trees: 78 apples → Ratio = \( \frac{78}{6} = 13 \)
- For 10 trees: 130 apples → Ratio = \( \frac{130}{10} = 13 \)
- For 12 trees: 156 apples → Ratio = \( \frac{156}{12} = 13 \)

Since the ratio of apples to trees is the same (13) for all entries, we conclude that the quantities in the data table are in a proportional relationship.

The correct response is:

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