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
12
Start Fraction 1 over 2 End Fraction
23
Start Fraction 2 over 3 End Fraction
32
Start Fraction 3 over 2 End Fraction
2
2
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The constant of proportionality can be found by examining the ratio of the y-coordinates to the corresponding x-coordinates.
Between the points (0,0) and (2,3), the ratio of the y-coordinate to the x-coordinate is 3/2.
Similarly, between the points (2,3) and (4,6), the ratio of the y-coordinate to the x-coordinate is also 3/2.
Therefore, the constant of proportionality is 3/2.
To identify the constant of proportionality from the graph, we need to determine the relationship between the x-values and the y-values of the plotted points. The constant of proportionality represents the ratio between the change in y-values and the change in x-values.
In this case, we can calculate the constant of proportionality by finding the slope of the line. The slope is defined as the change in y divided by the change in x.
Using the plotted points (0,0), (2,3), and (4,6), we can calculate the slope as follows:
Slope = (change in y) / (change in x)
= (6 - 0) / (4 - 0)
= 6 / 4
= 3 / 2
Therefore, the constant of proportionality from the graph is 3/2.
To identify the constant of proportionality from the graph, we can use the formula y = kx, where y represents the y-coordinate, x represents the x-coordinate, and k represents the constant of proportionality.
Looking at the plotted points on the graph, we can calculate the constant of proportionality by comparing the ratio of the y-coordinates to the x-coordinates:
For the first point (0, 0):
k = 0/0 (The line passes through the origin, so the ratio is undefined.)
For the second point (2, 3):
k = 3/2 = 1.5
For the third point (4, 6):
k = 6/4 = 1.5
Since the ratio of the y-coordinates to the x-coordinates is the same for both points (2,3) and (4,6), we can conclude that the constant of proportionality from the graph is 1.5 or in fraction form, "3/2".
Therefore, the correct answer is (3/2).