Graphs of Proportional Relationships Quick Check
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Question
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 relationship is proportional.
The relationship is proportional.
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 does not pass through the origin.
The relationship is non-proportional; the graph does not pass through the origin.
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The relationship is proportional.
To determine if the relationship is proportional, we need to check if the ratio of calories burned to time walking is constant. Let's calculate the ratio for each pair of values:
Ratio for 20 minutes: 100/20 = 5
Ratio for 30 minutes: 150/30 = 5
Ratio for 40 minutes: 200/40 = 5
Ratio for 60 minutes: 300/60 = 5
Ratio for 80 minutes: 400/80 = 5
As we can see, the ratio of calories burned to time walking is always 5. Therefore, the relationship is proportional.
Answer: The relationship is proportional.
To determine if the relationship between the amount of time spent walking and the number of calories burned is proportional, we need to check if the ratios of time to calories burned remain constant.
First, let's calculate the ratios for each pair of values in the table:
For 20 minutes of walking: 100 calories / 20 minutes = 5 calories/minute
For 30 minutes of walking: 150 calories / 30 minutes = 5 calories/minute
For 40 minutes of walking: 200 calories / 40 minutes = 5 calories/minute
For 60 minutes of walking: 300 calories / 60 minutes = 5 calories/minute
For 80 minutes of walking: 400 calories / 80 minutes = 5 calories/minute
As we can see, the ratio of calories burned to time spent walking is constant at 5 calories/minute. Therefore, the relationship between the amount of time spent walking and the number of calories burned is proportional.
So, the correct answer is:
The relationship is proportional.