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
12
Start Fraction 1 over 2 End Fraction
2
2
23
Start Fraction 2 over 3 End Fraction
32
Start Fraction 3 over 2 End Fraction
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To identify the constant of proportionality from the graph, we can look at the relationship between the x-values and the y-values. We can see that as the x-values increase by 2 (0 to 2 to 4), the y-values increase by 3 (0 to 3 to 6). This means that for every increase of 2 units in the x-direction, there is an increase of 3 units in the y-direction. Therefore, the constant of proportionality is 3/2 or 1.5.
So, the correct answer is:
Start Fraction 3 over 2 End Fraction
To identify the constant of proportionality from the graph, we need to determine the ratio of the change in y-values to the change in x-values between any two points on the line.
In this case, let's consider the points (0, 0), (2, 3), and (4, 6).
The change in y-values from (0, 0) to (2, 3) is 3 - 0 = 3.
The change in x-values from (0, 0) to (2, 3) is 2 - 0 = 2.
The ratio of the change in y-values to the change in x-values is 3/2.
Similarly, the change in y-values from (2, 3) to (4, 6) is 6 - 3 = 3, and the change in x-values is 4 - 2 = 2.
The ratio of the change in y-values to the change in x-values is again 3/2.
Since the ratios are the same for any two points on the line, the constant of proportionality is 3/2.
Therefore, the correct answer is 3/2.
To identify the constant of proportionality from the graph, we need to compare the ratio of the y-coordinates to the x-coordinates of the plotted points.
From the given points (0, 0), (2, 3), and (4, 6), we can see that:
For the point (0, 0), the ratio is 0/0, which is undefined.
For the point (2, 3), the ratio is 3/2, which simplifies to 1.5.
For the point (4, 6), the ratio is 6/4, which simplifies to 1.5 as well.
Since the ratio of the y-coordinates to the x-coordinates is the same (1.5) for all three points, the constant of proportionality from the graph is 1.5, which can be expressed as the fraction 3/2.
Therefore, the correct answer is: Start Fraction 3 over 2 End Fraction.
Use the image to answer the question.
A graph shows an x-axis representing time in seconds ranging from 0 to 12 in increments of 2. The y-axis represents heartbeats ranging from 0 to 18 in increments of 3. The graph shows a line representing resting heart rate.
What is the average number of heartbeats per second?
(1 point)
Responses
3 beats per second
3 beats per second
2 beats per second
2 beats per second
23 beat per second
Start Fraction 2 over 3 End Fraction beat per second
112 beats per second
1 Start Fraction 1 over 2 End Fraction beats per second
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To find the average number of heartbeats per second, we need to calculate the slope of the line on the graph. The slope represents the change in y-values (heartbeats) divided by the change in x-values (time in seconds).
From the graph, we can see that the line passes through the points (0, 0) and (12, 18). The change in y-values is 18 - 0 = 18, and the change in x-values is 12 - 0 = 12.
The slope is calculated by dividing the change in y-values by the change in x-values:
slope = change in y / change in x = 18 / 12 = 3/2 = 1.5
Therefore, the average number of heartbeats per second is 1.5 beats per second.
So, the correct answer is: Start Fraction 2 over 3 End Fraction beats per second.
Use the image to answer the question.
A figure shows four graphs labeled A, B, C, and D, each with an x and y axis and 0 at the origin, and each showing a curve. Graph A shows a straight line with a negative slope having x and y intercepts. Graph B shows a straight line with a positive slope having a y intercept above origin. Graph C shows an increasing concave up curve initiating at the origin. Graph D shows a straight line with a unit slope.
Decide which graph shows a proportional relationship.
(1 point)
Responses
A
A
C
C
B
B
D
D
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To determine which graph shows a proportional relationship, we need to look for a straight line on the graph.
From the given options, only Graph D shows a straight line (with a unit slope). This indicates a constant rate of change between the x and y values, which is characteristic of a proportional relationship.
Therefore, the graph that shows a proportional relationship is Graph D.
So, the correct answer is: D.
Use the image to answer the question.
A graph with x and y axes shows four curves labeled A, B, C, and D. Curve A has a step-like structure initiating at the origin, increasing steadily, tapering to a point, and again increasing. Curve B begins at the origin and is an increasing concave down curve. Curve C is a straight line with a unit slope. Curve D is a straight line that initiates at a point on the y-axis and then increases steadily.
Identify the proportional relationship from the graph.
(1 point)
Responses
Graph B
Graph B
Graph C
Graph C
Graph D
Graph D
Graph A
Graph A
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To identify the proportional relationship from the graph, we need to look for a straight line. From the given options, only Curve C represents a straight line with a unit slope. This indicates a constant rate of change between the x and y values, which is characteristic of a proportional relationship.
Therefore, the proportional relationship from the graph is represented by Curve C.
So, the correct answer is: Graph C.
Use the table to answer the question.
Time walking (minutes) 20 30 40 60 80
Calories burned 100 150 200 300 400
The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.
(1 point)
Responses
The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph would be an arc.
The proportional relationship cannot be determined from the information provided.
The proportional relationship cannot be determined from the information provided.
The relationship is proportional.
The relationship is proportional.
The relationship is non-proportional; the graph does not pass through the origin.