Time walking. Calories

burned

20. 100
30. 150
40. 200
60. 300
80. 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
A. The relationship Non proportional The graph would be an arc
B The proportional relationship cannot be determined from the information provided
C Is the relationship Is non proportional the Graph does not Pass through the origin
D The relationship is proportional

1 answer

To determine if the relationship between time walking and calories burned is proportional, we need to assess whether the ratio of calories burned to time is constant.

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

  1. For 20 minutes: \( \frac{100}{20} = 5 \)
  2. For 30 minutes: \( \frac{150}{30} = 5 \)
  3. For 40 minutes: \( \frac{200}{40} = 5 \)
  4. For 60 minutes: \( \frac{300}{60} = 5 \)
  5. For 80 minutes: \( \frac{400}{80} = 5 \)

Since the ratio is constant at 5 for all time intervals, the relationship is indeed proportional.

Additionally, we can check whether the graph passes through the origin. When time is 0, if calories burned is also 0, it will pass through the origin, indicating that the relationship is proportional.

Based on this analysis, the correct answer is:

D. The relationship is proportional.