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 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.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to check if there is a constant ratio between the numbers of trees and the numbers of apples.

The pairs from the table are:

- (2, 26)
- (3, 39)
- (6, 78)
- (10, 130)
- (12, 156)

Now, let's calculate the ratios of apples to trees for each pair:

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 the ratio for all pairs is constant (13), the quantities in the data table are in a proportional relationship.

Therefore, the response is:

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