# 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.
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 data table does not have a proportional relationship because the ratios of apples to trees are not equivalent for each set of numbers.
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 trees to the number of apples is the same for all the pairs.
To find the ratio for each pair, we divide the number of apples by the number of trees:
For the pair (2 trees, 26 apples): 26/2 = 13
For the pair (3 trees, 39 apples): 39/3 = 13
For the pair (6 trees, 78 apples): 78/6 = 13
For the pair (10 trees, 130 apples): 130/10 = 13
For the pair (12 trees, 156 apples): 156/12 = 13
Since the ratio of apples to trees is the same (13) for all the pairs, we can conclude that the quantities in the data table are in a proportional relationship.
Therefore, the correct response is: Yes, the data table has a proportional relationship.