George observes that for every increase of 1 in the value of x, there is an increase of 60 in the corresponding value of y. He claims that this means the relationship represented by the table is proportional. Is George correct, saying that this table represents a proportional relationship? Why or why not?
Table:
x 1 2 3 4 5
y 90 150 210 270 330
To determine whether the relationship represented by the table is proportional, we need to check if the ratio between the corresponding values of x and y remains constant.
Let's calculate the ratios for each pair of values in the table:
For x = 1 and y = 90: y/x = 90/1 = 90
For x = 2 and y = 150: y/x = 150/2 = 75
For x = 3 and y = 210: y/x = 210/3 = 70
For x = 4 and y = 270: y/x = 270/4 = 67.5
For x = 5 and y = 330: y/x = 330/5 = 66
As seen from the calculations, the ratios are not equal. In a proportional relationship, the ratio between the corresponding values should be the same for all pairs. In this case, the ratios are different, which means the relationship is not proportional.
Therefore, George is not correct in claiming that the table represents a proportional relationship.