We have from the graph, that this is a proportional relationship: the graph passes through the point (0, 0).
• Variable y ---> Costs ($)
,• Variable x ---> Number of Juice Drinks Purchased
We have the following statements:
1. Point M represents the cost of buying 3 juice drinks. This is TRUE. We have that the x-value for point M is (3, 14), that is, about $14.
2. It costs about $90 to purchase 20 juice drinks. We can solve this question having that the proportional relationship is given by:
[tex]\frac{y}{x}=\frac{40}{9}=4.444444\ldots[/tex]Since we have that buying 9 juice drinks costs about $40 (from the graph). We can see this from the coordinates (9, 40).
Therefore, for 20 juice drinks, we have:
[tex]\frac{y}{x}=4.444444\ldots\Rightarrow y=4.444444\ldots\cdot x\Rightarrow y=4.444444\cdot20\Rightarrow y=88.8888\ldots[/tex]This second statement is TRUE. It will cost about $90 ($88.89) to buy 20 juice drinks.
3. It costs about $2 to purchase 9 juice drinks. We can proceed as before:
[tex]\frac{y}{x}=4.44444\ldots\Rightarrow y=4.44444\cdot x\Rightarrow y=4.44444\cdot9\Rightarrow y=39.9999\ldots[/tex]This statement is FALSE. It will cost about $40 to purchase 9 juice drinks. (We can also check this from the graph, x = 9, y is, approximately, equal to 40.)
In summary, we have:
• Point M represents the cost of buying 3 juice drinks., ,This is TRUE,.
,• It costs about $90 to purchase 20 juice drinks,. ,This is TRUE,.
,• It costs about $2 to purchase 9 juice drinks,. ,This is FALSE,.
