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
12
Start Fraction 1 over 2 End Fraction
32
Start Fraction 3 over 2 End Fraction
2
2
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The constant of proportionality from the graph can be identified as 2/3.
To determine the constant of proportionality from the graph, we can use the points that the line passes through.
The points are: (0, 0), (2, 3), and (4, 6).
We can calculate the change in y-values over the change in x-values for any two of these points.
For example, using the points (0, 0) and (2, 3):
Change in y = 3 - 0 = 3
Change in x = 2 - 0 = 2
So, the ratio of the change in y to the change in x is 3/2.
Therefore, the constant of proportionality from the graph is 3/2.
To find the constant of proportionality from the graph, we can use the formula for the equation of a straight line, which is given by y = mx + b, where m represents the slope (constant of proportionality in this case) and b represents the y-intercept.
From the graph, we can see that the line passes through the points (0, 0), (2, 3), and (4, 6).
We can find the slope (m) by using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate:
m = (6 - 0) / (4 - 0)
m = 6 / 4
m = 3/2
Therefore, the constant of proportionality from the graph is 3/2.