Question

jonahs 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 table shows the relationship between the number of additional gigabytes of data jonah uses in a month, x, and the total amount (in dollars) of his bill, y.

x (additional gigabytes)	y (dollars)
2.4	$43
3.2	$48
4	$53

according to the values in the table, do x and y have a proportional relationship?
yes
no

Explanation:

Step1: Recall proportional - relationship condition

For a proportional relationship between $x$ and $y$, the ratio $\frac{y}{x}$ must be constant for all non - zero values of $x$.

Step2: Calculate ratios for each data pair

For the first pair $(x_1 = 0.8,y_1 = 33)$, the ratio is $\frac{y_1}{x_1}=\frac{33}{0.8}=\frac{330}{8} = 41.25$.
For the second pair $(x_2 = 2.4,y_2 = 43)$, the ratio is $\frac{y_2}{x_2}=\frac{43}{2.4}=\frac{430}{24}=\frac{215}{12}\approx17.92$.
Since $\frac{33}{0.8}
eq\frac{43}{2.4}$, the ratios are not constant.

Answer:

no