# The graph shows the number of teaspoons of lemon juice in cups of lemonade. Which ordered pair represents a ratio equivalent to the ratio of teaspoons of lemon juice to cups of lemonade shown by the point on the graph? A. (4,16) B. (6,1) C. (9,3) D. (16,4) Oscar chose A as the correct answer. How did he get that answer?

Question
Linear equations and graphs
The graph shows the number of teaspoons of lemon juice in cups of lemonade.
Which ordered pair represents a ratio equivalent to the ratio of teaspoons of lemon juice to cups of lemonade shown by the point on the graph?
A. (4,16)
B. (6,1)
C. (9,3)
D. (16,4)
Oscar chose A as the correct answer. How did he get that answer?

2020-12-07
The ordered pair in the graph is (8,2). Since x represents the number of teaspoons of lemon juice and y represents the number of cups of lemonade, then the ordered pair (8,2) means the ratio of teaspoons of lemon juice to cups of lemonade is 8 teaspoons of lemon juice : 2 cups of lemonade.
Dividing both numbers in the ratio of 8 teaspoons of lemon juice to 2 cups of lemonade by 2 then gives the ratio 4 teaspoons of lemon juice to 1 cup of lemonade.
An ordered pair will then represent an equivalent ratio if the number of teaspoons (the x-coordinate) is 4 times the number of cups of lemonade (the y-coordinate).
The correct ordered pair is then D. (16,4) . since the x-coordinate of 16 is four times the y-coordinate of 4.
If Oscar chose A as the correct answer, then he switched the ratio. He used a ratio of 1 teaspoon of lemon juice : 4 cups of lemonade since he chose an ordered pair that had a number of cups of lemonade that was 4 times the number of teaspoons of lemon juice.

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