Use the table to answer the question.

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 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 would be an arc.
The relationship is non-proportional; the graph would be an arc.

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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Answer 1

To determine if the relationship between the time walking (in minutes) and the calories burned is proportional, we need to check if the ratio of calories burned to time walking is constant for all the values given.

Let's calculate the ratio of calories burned to time walking for each entry:

• For 20 minutes: \( \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \)
• For 30 minutes: \( \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \)
• For 40 minutes: \( \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \)
• For 60 minutes: \( \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \)
• For 80 minutes: \( \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \)

Since the ratio is constant (5 calories per minute) for all time intervals, this indicates that the relationship is proportional.

Therefore, the correct response is: The relationship is proportional.