Use the image to answer the question.
Identify the constant of proportionality from the graph.
(1 point)
Responses
32
Start Fraction 3 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
23
Start Fraction 2 over 3 End Fraction
2
2
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To answer this question, we need to determine the ratio between the y-values and the x-values. Looking at the graph, we can see that for every increase of 1 in the x-value, the y-value increases by a constant amount. In this case, the ratio is 2, which means the constant of proportionality is 2. Therefore, the correct answer is 2.
Use the image to answer the question.
What is the average number of heartbeats per second?
(1 point)
Responses
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
3 beats per second
To find the average number of heartbeats per second, we need to calculate the slope of the line on the graph. The slope represents how much the y-values change for every change in the x-values.
Looking at the graph, we can see that the line goes through the points (0,0) and (3,6). The y-value increases by 6 when the x-value increases by 3.
To find the average number of heartbeats per second, we can divide the change in y-values by the change in x-values:
Change in y-values: 6
Change in x-values: 3
Average number of heartbeats per second = (Change in y-values) / (Change in x-values) = 6/3 = 2
Therefore, the average number of heartbeats per second is 2 beats per second.
Graphs of Proportional Relationships Quick Check
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Question
Use the image to answer the question.
Decide which graph shows a proportional relationship.
(1 point)
Responses
C
C
A
A
B
B
D
D
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1
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2
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3
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4
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To determine which graph shows a proportional relationship, we need to see if the graph represents a straight line that passes through the origin (0,0).
Looking at the options, we can see that graph B represents a straight line passing through the origin. This indicates that graph B shows a proportional relationship.
Therefore, the correct answer is B.
Use the image to answer the question.
Identify the proportional relationship from the graph.
(1 point)
Responses
Graph D
Graph D
Graph A
Graph A
Graph B
Graph B
Graph C
To identify the proportional relationship from the graph, we need to determine if the graph represents a straight line passing through the origin (0,0).
Looking at the options, we can see that graph A represents a straight line passing through the origin. This indicates that graph A shows a proportional relationship.
Therefore, the correct answer is Graph A.
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 proportional relationship cannot be determined from the information provided.
The proportional relationship cannot be determined from the information provided.
The relationship is non-proportional; the graph would be an arc.
The relationship is non-proportional; the graph would be an arc.
The relationship is proportional.
The relationship is proportional.
The relationship is non-proportional; the graph does not pass through the origin.
To determine if the relationship is proportional, we need to check if there is a constant ratio between the time spent walking and the number of calories burned.
Let's calculate the ratios between the time and calories burned:
20 minutes: 100 calories = 1:5
30 minutes: 150 calories = 1:5
40 minutes: 200 calories = 1:5
60 minutes: 300 calories = 1:5
80 minutes: 400 calories = 1:5
We can see that there is a constant ratio of 1:5 between the time and calories burned. This indicates that the relationship is indeed proportional.
Therefore, the correct answer is: The relationship is proportional.
To identify the constant of proportionality from the graph, you need to determine the relationship between the x-values and the corresponding y-values.
The constant of proportionality represents the ratio between the x-values and the y-values in any given point or pair of points on the graph.
To calculate the constant of proportionality, choose any two points on the line and calculate the ratio of the change in y-values to the change in x-values.
In the given image, it is not possible to directly determine the constant of proportionality without additional context or data. Therefore, none of the provided options -- 32, 3/2, 12, 1/2, 23, 2/3, 2 -- can be considered the correct answer.
To find the constant of proportionality from a graph, you usually need more information or a specific equation representing the relationship between the x and y values.