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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anonymous
asked
To determine the ratio between the x-values and y-values for Option A, we can divide the y-value by the x-value for each coordinate pair:
For the first coordinate pair: 5/12 = 0.4167
For the second coordinate pair: 10/24 = 0.4167
For the third coordinate pair: 15/36 = 0.4167
The ratio between the x-values and y-values for Option A is approximately 0.4167.
To maintain this ratio for Option B, we can multiply the x-value of the last coordinate pair for Option A (27) by 0.4167 to find the corresponding y-value:
27 * 0.4167 = 11.2509
Since the y-values are rounded to the nearest dollar, the next coordinate pair for Option B that would keep the ratio the same is (-27, 11). However, this option is not listed as a choice.
The closest coordinate pair to the calculated value is (29, 20), so the correct answer is:
(29, 20)
left parenthesis 29 comma 20 right parenthesis