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Graphs of Proportional Relationships Quick Check
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Question
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
The constant of proportionality from the graph is 2.
To identify the constant of proportionality from the graph, we can look at the rate of change of the line. The constant of proportionality represents the ratio of the change in the dependent variable (y) to the change in the independent variable (x).
In this case, we can find the rate of change by selecting any two points on the line. Let's choose the points (0, 0) and (2, 3).
The change in y is 3 - 0 = 3, and the change in x is 2 - 0 = 2.
Therefore, the constant of proportionality is 3/2 or Start Fraction 3 over 2 End Fraction.
So, the correct answer is Start Fraction 3 over 2 End Fraction.
To identify the constant of proportionality from the given graph, we need to look at how the y-values change as the x-values change. The constant of proportionality represents the rate at which the y-values change for every unit change in the x-values.
Looking at the plotted points on the graph, we can see that as x increases by 2 units, y increases by 3 units. Similarly, as x increases by 2 units again, y increases by 3 units again. This consistent pattern tells us that the constant of proportionality is 3/2.
Therefore, the correct response is "Start Fraction 3 over 2 End Fraction".