Using Ratios in the Coordinate Plane Quick Check
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Question
Use the image to answer the question.
A graph with the x-axis representing oranges ranging from 0 to 36 in increments of 3 and the y-axis representing dollars ranging from 0 to 20 in increments of 1 shows six plotted points, 3 each for option A and option B. Option A has the following points: left parenthesis 12 comma 5 right parenthesis; left parenthesis 24 comma 10 right parenthesis; and left parenthesis 36 comma 15 right parenthesis. Option B has the following points: left parenthesis 9 comma 6 right parenthesis; left parenthesis 18 comma 12 right parenthesis; and left parenthesis 27 comma 18 right parenthesis.
Which coordinate pair should be plotted next for Option B to keep the ratio the same?
(1 point)
Responses
(33, 24)
left parenthesis 33 comma 24 right parenthesis
(30, 21)
left parenthesis 30 comma 21 right parenthesis
(29, 20)
left parenthesis 29 comma 20 right parenthesis
(36, 24)
left parenthesis 36 comma 24 right parenthesis
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To find the ratio of dollars to oranges for option A and option B, we can compare the y-coordinates (dollars) to the x-coordinates (oranges).
For option A, the ratio is 5/12 = 10/24 = 15/36.
To keep the ratio the same, we need to find the corresponding y-coordinate for an x-coordinate of 9 (since the x-coordinate of the next point for option B is 9).
Using the ratio, we can set up a proportion:
5/12 = y/9
Cross-multiplying, we get:
12y = 45
Solving for y, we get:
y = 45/12 = 15/4 = 3.75
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is (9, 3.75).
None of the given answer choices match this coordinate pair, so none of the options are correct.