Use the table to answer the question. Time walking (minutes): 20, 30, 40, 60, 80 Calories burned: 100, 150, 200, 300, 400

Question

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 proportional relationship cannot be determined from the information provided.
B. The relationship is non-proportional; the graph would be an arc.
C. The relationship is proportional.
D. The relationship is non-proportional; the graph does not pass through the origin.

Answer 1

To determine if the relationship is proportional, we need to check if the ratio of calories burned to time walking is constant for all given data points.

Here are the calculations for each pair of time and calories:

1. For 20 minutes:

   • \( \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \text{ calories per minute} \)

2. For 30 minutes:

   • \( \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \text{ calories per minute} \)

3. For 40 minutes:

   • \( \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \text{ calories per minute} \)

4. For 60 minutes:

   • \( \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \text{ calories per minute} \)

5. For 80 minutes:

   • \( \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \text{ calories per minute} \)

Since the ratio of calories burned to time walking is constant at \(5\) for all data points, the relationship is proportional.

Therefore, the answer is: C. The relationship is proportional.