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 A to keep the ratio the same?
(1 point)
Responses
(40, 19)
left parenthesis 40 comma 19 right parenthesis
(48, 20)
left parenthesis 48 comma 20 right parenthesis
(37, 16)
left parenthesis 37 comma 16 right parenthesis
(41, 20)
left parenthesis 41 comma 20 right parenthesis
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In order to find the coordinates that should be plotted next for Option A to keep the ratio the same, we need to examine the pattern between the x-values (oranges) and y-values (dollars).
Let's calculate the ratio for each point:
12/5 = 2.4
24/10 = 2.4
36/15 = 2.4
The ratio for Option A is consistently 2.4.
Now let's calculate the ratio for the current points in Option B:
9/6 = 1.5
18/12 = 1.5
27/18 = 1.5
The ratio for Option B is consistently 1.5.
To keep the ratio the same as Option A (2.4), we need to find a coordinate pair where the ratio is also 2.4. Checking the given options, we find that the coordinate pair (40, 19) has a ratio of 40/19 ≈ 2.105, which is not the same as the desired ratio.
Therefore, none of the given options have the correct coordinate pair that will keep the ratio the same as Option A.