Question

khalils smartphone plan with stark mobile includes unlimited talk and text and a certain amount of data every month. if he uses additional data, he is charged more on his bill. this graph shows the relationship between the number of additional gigabytes of data khalil uses in a month, x, and the total amount (in dollars) of his bill, y. do x and y have a proportional relationship?

Explanation:

Step1: Recall proportional relationship

A proportional relationship between two variables \( x \) and \( y \) is of the form \( y = kx \) (where \( k \) is a constant), and its graph passes through the origin \((0,0)\).

Step2: Analyze the given graph

Looking at the graph, when \( x = 0 \) (no additional gigabytes used), the value of \( y \) (total bill) is not \( 0 \) (it is around \( 45 \) dollars). So the graph does not pass through the origin.

Step3: Conclusion

Since a proportional relationship requires the graph to pass through the origin (\( y = 0 \) when \( x = 0 \)) and this graph does not, \( x \) and \( y \) do not have a proportional relationship.

Answer:

No, \( x \) and \( y \) do not have a proportional relationship because the graph of their relationship does not pass through the origin \((0,0)\) (when \( x = 0 \), \( y
eq0\)).