The quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship.
In order to determine if the data table represents a proportional relationship, we need to compare the ratio of the quantities in the table.
Let's take two sets of values from the table and calculate their ratios:
1) Quantity A = 5, Quantity B = 20
Ratio = Quantity B / Quantity A = 20 / 5 = 4
2) Quantity A = 10, Quantity B = 40
Ratio = Quantity B / Quantity A = 40 / 10 = 4
As we can see, in both cases, the ratios are equal to 4.
Thus, since the ratio of the quantities remains constant (equal to 4) for different values in the table, we can conclude that the table represents a proportional relationship.