# of Trees
2, 3, 6, 10, 12
# of Apples
26, 39, 78, 130, 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
Options:
No, the ratio 6 : 78 is not proportional to the other ratios
Yea, the data table has a proportional relationship
No, the ratios are not equivalent
No, the table does not count consecutively
No, the ratios are not equivalent
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 consistent throughout the table.
Let's calculate the ratios for each pair of values in the table:
Ratio for 2 trees and 26 apples: 2/26 = 1/13
Ratio for 3 trees and 39 apples: 3/39 = 1/13
Ratio for 6 trees and 78 apples: 6/78 = 1/13
Ratio for 10 trees and 130 apples: 10/130 = 1/13
Ratio for 12 trees and 156 apples: 12/156 = 1/13
As we can see, all the ratios are equal to 1/13. Therefore, the quantities in the data table are in a proportional relationship.
Therefore, the correct option is: "Yea, the data table has a proportional relationship."
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the # of Trees and the # of Apples are consistent.
To find the ratios, we can divide the # of Apples by the # of Trees for each corresponding entry in the table:
For the first entry: 26 / 2 = 13
For the second entry: 39 / 3 = 13
For the third entry: 78 / 6 = 13
For the fourth entry: 130 / 10 = 13
For the fifth entry: 156 / 12 = 13
As we can see, the ratios in each case are all equal to 13. This means that the quantities in the data table have a proportional relationship. Therefore, the correct option is:
Yes, the data table has a proportional relationship