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?
not proportional, but linear
y = 60x is proportional
y=60x+3 is not proportional, but is linear, with the same slope of m=60
To determine whether the relationship represented by the table is proportional, we need to check if the ratio between the changes in x and y values remains constant.
First, let's calculate the ratio between the changes in x and y values. We are given that for every increase of 1 in x, there is an increase of 60 in y. So, the ratio is:
Ratio = Change in y / Change in x = 60/1 = 60
Now, let's check if this ratio remains constant for all values in the table.
For example, when x increases by 2, we would expect y to increase by 2 * 60 = 120. Let's verify this:
x = 1, y = 60 (initial values)
x = 2, y = 60 + 120 = 180
The ratio for this case is:
Ratio = (180 - 60) / (2 - 1) = 120 / 1 = 120
Since the ratio is 120, which is different from the initial ratio of 60, we can conclude that the relationship represented by the table is not proportional.
Therefore, George's claim that the relationship is proportional is incorrect.
No, George is not correct in claiming that the relationship represented by the table is proportional. A proportional relationship implies that for every increase in the independent variable (x), the dependent variable (y) increases or decreases by a constant ratio. In a proportional relationship, the ratio of y to x remains the same throughout.
However, in this case, the relationship between x and y is not proportional because the increase in y (60) is not a constant ratio of the increase in x (1). In a proportional relationship, the ratio of y to x should always be the same. For example, if for every increase of 1 in x, y increased by 60, the ratio of y to x would be 60:1. But, since the ratio is not constant and changes depending on the values of x and y, it is not a proportional relationship.