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A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
identify the constant of proportionality from the graph.
(1 point)
Responses
32
Start Fraction 3 over 2 End Fraction
2
2
23
Start Fraction 2 over 3 End Fraction
12
The constant of proportionality from the graph is 2.
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I apologize for the confusion, but none of the provided responses accurately represent the constant of proportionality from the graph.
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To identify the constant of proportionality from the graph, we need to determine the relationship between the x-values and y-values.
First, let's calculate the change in y (Δy) and the change in x (Δx) for each set of plotted points:
- Δy = 3 - 0 = 3
- Δx = 2 - 0 = 2
- Δy = 6 - 3 = 3
- Δx = 4 - 2 = 2
Next, let's determine the ratio between Δy and Δx for both sets of plotted points:
- Ratio 1 = Δy/Δx = 3/2 = 1.5
- Ratio 2 = Δy/Δx = 3/2 = 1.5
We notice that the ratio between Δy and Δx is consistent for both sets of plotted points. Therefore, the constant of proportionality from the graph is
Start Fraction 3 over 2 End Fraction
To identify the constant of proportionality from the graph, we need to examine the relationship between the x-values and y-values of the plotted points.
Given the points (0,0), (2,3), and (4,6), we can calculate the change in y (∆y) and the change in x (∆x) for each pair of points.
∆y = y2 - y1
∆x = x2 - x1
Using the coordinates (0,0) and (2,3):
∆y = 3 - 0 = 3
∆x = 2 - 0 = 2
Using the coordinates (2,3) and (4,6):
∆y = 6 - 3 = 3
∆x = 4 - 2 = 2
Notice that for both pairs of points, ∆y/∆x = 3/2.
The constant of proportionality is the ratio between ∆y and ∆x, which remains constant as long as the relationship between x and y is proportional. In this case, the constant of proportionality is 3/2.
Therefore, the correct answer is "Start Fraction 3 over 2 End Fraction".