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

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.
No, the table does not count consecutively.

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

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 need to check if the ratios of the number of apples to the number of trees are constant.

Looking at the data:

- For 2 trees, the ratio is 26 apples / 2 trees = 13 apples per tree.
- For 3 trees, the ratio is 39 apples / 3 trees = 13 apples per tree.
- For 6 trees, the ratio is 78 apples / 6 trees = 13 apples per tree.
- For 10 trees, the ratio is 130 apples / 10 trees = 13 apples per tree.
- For 12 trees, the ratio is 156 apples / 12 trees = 13 apples per tree.

Since the ratio (apples per tree) is constant at 13 for all entries, the data table does indeed have a proportional relationship.

The correct response is:

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