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.

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.

Answer 1

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 constant.

Let's calculate the ratios for each pair of data points:
- For the first pair (2 trees and 26 apples), the ratio is 26/2 = 13.
- For the second pair (3 trees and 39 apples), the ratio is 39/3 = 13.
- For the third pair (6 trees and 78 apples), the ratio is 78/6 = 13.
- For the fourth pair (10 trees and 130 apples), the ratio is 130/10 = 13.
- For the fifth pair (12 trees and 156 apples), the ratio is 156/12 = 13.

Since all the ratios are equal to 13, the quantities in the data table are in a proportional relationship. The ratio of the number of trees to the number of apples is constant.

Answer 2

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 constant.

In this case, let's calculate the ratios for each data point:

For the first data point (2 trees, 26 apples): 2/26 = 1/13

For the second data point (3 trees, 39 apples): 3/39 = 1/13

For the third data point (6 trees, 78 apples): 6/78 = 1/13

For the fourth data point (10 trees, 130 apples): 10/130 = 1/13

For the fifth data point (12 trees, 156 apples): 12/156 = 1/13

As we can see, in every case, the ratio is 1/13. Thus, the quantities in the data table are in a proportional relationship.

Answer 3

To determine if the quantities in the data table are in a proportional relationship, we can check if the ratio of "number of apples" to "number of trees" remains constant.

Let's calculate the ratios 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 ratio of "number of apples" to "number of trees" is constant (13) for all the rows, we can conclude that the quantities in the data table are in a proportional relationship.