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
32
Start Fraction 3 over 2 End Fraction
23
Start Fraction 2 over 3 End Fraction
12
Start Fraction 1 over 2 End Fraction
2
2
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The constant of proportionality can be found by examining the graph and determining the change in y-values for a given change in x-values.
In this graph, as the x-values increase by 2 (from 0 to 2 to 4), the corresponding y-values increase by 3 (from 0 to 3 to 6).
Therefore, the constant of proportionality is 3/2.
To identify the constant of proportionality from the graph, we need to find the ratio between the change in the y-values to the corresponding change in the x-values for any two points on the line.
Let's take the points (0, 0) and (2, 3) on the line. The change in the y-values is 3 - 0 = 3, and the change in the x-values is 2 - 0 = 2.
So, the ratio is 3/2.
Therefore, the constant of proportionality from the graph is 3/2.
To identify the constant of proportionality from the graph, we need to analyze the relationship between the x-values and the y-values of the plotted points.
The constant of proportionality is the ratio between the change in the y-values and the change in the x-values. In other words, it represents how much the y-value changes for every 1 unit increase in the x-value.
Looking at the plotted points (0, 0), (2, 3), and (4, 6), we can see that for every increase of 2 units in the x-value, the corresponding y-value increases by 3 units.
This means that for every 1 unit increase in the x-value, the corresponding y-value increases by 3/2 units.
Therefore, the constant of proportionality from the graph is 3/2.
So the correct answer is: Start Fraction 3 over 2 End Fraction.