Use the image to answer the question.
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
23
Start Fraction 2 over 3 End Fraction
2
2
12
Start Fraction 1 over 2 End Fraction
32
Start Fraction 3 over 2 End Fraction
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From the given information, we can see that the points (2, 3) and (4, 6) are on the line. To find the constant of proportionality, we can calculate the ratio of the change in y-coordinates to the change in x-coordinates.
The change in y-coordinates is 6 - 3 = 3.
The change in x-coordinates is 4 - 2 = 2.
So, the constant of proportionality is 3/2 or Start Fraction 3 over 2 End Fraction.
To identify the constant of proportionality from the graph, we can look at the relationship between the x-values and y-values.
From the plotted points, we can see that the y-values increase by a constant rate as the x-values increase.
If we compare the change in y-values to the change in x-values for any two points, we can determine the constant of proportionality.
Let's compare the points (0, 0) and (2, 3):
Change in y = 3 - 0 = 3
Change in x = 2 - 0 = 2
Now, let's compare the points (2, 3) and (4, 6):
Change in y = 6 - 3 = 3
Change in x = 4 - 2 = 2
Since the change in y-values is always 3 times the change in x-values, the constant of proportionality is 3.
Therefore, the correct answer is Start Fraction 2 over 3 End Fraction.
To identify the constant of proportionality from the graph, we need to examine the relationship between the x and y values. The constant of proportionality is the ratio of the change in the y-values to the change in the x-values.
From the given plotted points, we can determine that the change in y (Δy) is 6 - 0 = 6, and the change in x (Δx) is 4 - 0 = 4.
To calculate the constant of proportionality, we divide the change in y by the change in x: Δy/Δx.
Therefore, the constant of proportionality is 6/4, which simplifies to 3/2.
Hence, the correct answer is: Start Fraction 3 over 2 End Fraction.