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
2
2
32
Start Fraction 3 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
23
Start Fraction 2 over 3 End Fraction
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The constant of proportionality can be found by finding the ratio of the y-values to the x-values.
From the graph, we can see that the ratio of the y-values to the x-values is always 3/2.
Therefore, the constant of proportionality from the graph is 3/2.
To identify the constant of proportionality from the graph, we can look at the relationship between the x-coordinate and the y-coordinate of each point.
From the given plotted points, we can see that as the x-coordinate increases by 2 (from 0 to 2), the y-coordinate increases by 3 (from 0 to 3). Similarly, as the x-coordinate increases by 2 again (from 2 to 4), the y-coordinate increases by 3 again (from 3 to 6).
This shows a consistent rate of change, where for every 2 unit increase in the x-coordinate, there is a 3 unit increase in the y-coordinate. Therefore, the constant of proportionality is 3/2.
To identify the constant of proportionality from the graph, we need to examine the relationship between the x-values and y-values of the plotted points.
The constant of proportionality, also known as the slope, can be determined by finding the change in y (Δy) divided by the change in x (Δx) between any two points on the line.
Let's calculate the change in y and change in x between the points (0,0) and (2,3):
Δy = 3 - 0 = 3
Δx = 2 - 0 = 2
Now, we can find the constant of proportionality by dividing the change in y by the change in x:
Constant of proportionality = Δy / Δx = 3 / 2 = 1.5
So, the correct answer is 1.5 (or written as a mixed number, 3/2).
Therefore, the correct response is "32 Start Fraction 3 over 2 End Fraction"
What is the average number of heartbeats per second?
(1 point)
Responses
112 beats per second
1 Start Fraction 1 over 2 End Fraction beats per second
23 beat per second
Start Fraction 2 over 3 End Fraction beat per second
2 beats per second
2 beats per second
3 beats per second