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 non-proportional; the graph does not pass through the origin.
The relationship is non-proportional; the graph does not pass through the origin.

The relationship is proportional.

1 answer

To determine if the relationship between the time walking and the calories burned is proportional, we can look for a constant ratio between the two variables—time and calories burned.

We can calculate the ratio of calories burned to time for each pair:

  • 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 of calories burned to time is consistent (always equal to 5), this indicates a proportional relationship.

Also, a proportional relationship passes through the origin, which is evident since when time is 0, the calories burned would equally be 0.

Therefore, the correct response is:

The relationship is proportional.