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

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 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 ratios are not equivalent.

Answer 1

To determine if the quantities in the data table represent a proportional relationship, we need to analyze the ratios of the number of apples to the number of trees.

We can find the ratio of apples to trees for each pair:

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

Since the ratio is consistently 13 for all pairs, we see that the quantities are in a proportional relationship.

Therefore, the correct response is:

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