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 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.
To determine if the quantities in the data table are in a proportional relationship, we need to examine the ratios of the number of trees to the number of apples for each data point.
Let's calculate the ratios for each row:
- For the first row: 2 trees to 26 apples = 2/26 = 1/13
- For the second row: 3 trees to 39 apples = 3/39 = 1/13
- For the third row: 6 trees to 78 apples = 6/78 = 1/13
- For the fourth row: 10 trees to 130 apples = 10/130 = 1/13
- For the fifth row: 12 trees to 156 apples = 12/156 = 1/13
As we can see, all the ratios are equal to 1/13. This means that regardless of the number of trees, the ratio of trees to apples remains constant at 1/13. Therefore, the quantities in the data table are in a proportional relationship.
Hence, the correct response would be:
Yes, the data table has a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we can calculate the ratios of the number of apples to the number of trees for each row.
For the first row: 26/2 = 13
For the second row: 39/3 = 13
For the third row: 78/6 = 13
For the fourth row: 130/10 = 13
For the fifth row: 156/12 = 13
Since the ratios are all equal to 13, the quantities in the data table are in a proportional relationship. Therefore, the correct response is:
Yes, the data table has a proportional relationship.