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
(36, 24)
left parenthesis 36 comma 24 right parenthesis
(33, 24)
left parenthesis 33 comma 24 right parenthesis
(29, 20)
left parenthesis 29 comma 20 right parenthesis
(30, 21)
left parenthesis 30 comma 21 right parenthesis
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you have to choose one the options shown
To determine the coordinate pair that should be plotted next for Option B to keep the ratio the same, we need to compare the ratio of change in the y-values to the ratio of change in the x-values.
For option A, the ratio of change in y-values is (10 - 5) / (24 - 12) = 5/12.
For option B, the ratio of change in y-values is (12 - 6) / (18 - 9) = 6/9 = 2/3.
To keep the ratio the same, the next coordinate pair for Option B should have the same ratio of change in y-values, which is 5/12.
Let's check the options:
Option 1: (36, 24)
The ratio of change in y-values would be (24 - 12) / (36 - 27) = 12/9 = 4/3, not equal to 5/12.
Option 2: (33, 24)
The ratio of change in y-values would be (24 - 12) / (33 - 27) = 12/6 = 2, not equal to 5/12.
Option 3: (29, 20)
The ratio of change in y-values would be (20 - 12) / (29 - 18) = 8/11, not equal to 5/12.
Option 4: (30, 21)
The ratio of change in y-values would be (21 - 12) / (30 - 18) = 9/12 = 3/4, not equal to 5/12.
None of the given options have the same ratio of change in y-values as the previous points for Option B. Therefore, we cannot determine the coordinate pair that should be plotted next to keep the ratio the same based on the given options and information.
Apologies for the confusion. Based on the given options, the closest option that fits the given ratio of change in y-values is:
Option 2: (33, 24)
The ratio of change in y-values would be (24 - 12) / (33 - 27) = 12/6 = 2, which is closest to the desired ratio of 5/12.
To answer this question, we need to examine the given information and analyze the pattern in the plotted points for Option B.
Option B has three plotted points: (9, 6), (18, 12), and (27, 18). The x-values in these points form the arithmetic sequence 9, 18, 27. Similarly, the y-values form the arithmetic sequence 6, 12, 18.
To keep the ratio between x and y values the same, we need to find the next value in both sequences. The common difference between the x-values is 18 - 9 = 9, and the common difference between the y-values is 12 - 6 = 6.
Adding the common difference, 9, to the last x-value, 27, we get 27 + 9 = 36. Therefore, the next x-value for Option B should be 36.
Adding the common difference, 6, to the last y-value, 18, we get 18 + 6 = 24. Therefore, the next y-value for Option B should be 24.
Therefore, the coordinate pair that should be plotted next for Option B to keep the ratio the same is (36, 24).
So, the correct answer is: (36, 24) or (36,24) in the format requested.