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To determine if the relationship between the time spent walking and the number of calories burned is proportional, we need to check if the ratio between time and calories burned remains constant.

Here’s the data from the table:

| Time walking (minutes) | Calories burned |
|------------------------|-----------------|
| 20                     | 100             |
| 30                     | 150             |
| 40                     | 200             |
| 60                     | 300             |
| 80                     | 400             |

Now, let’s calculate the ratio of calories burned per minute for each pair:

- \( \frac{100}{20} = 5 \)
- \( \frac{150}{30} = 5 \)
- \( \frac{200}{40} = 5 \)
- \( \frac{300}{60} = 5 \)
- \( \frac{400}{80} = 5 \)

Since the ratio is constant at 5 calories per minute, the relationship is proportional. A proportional relationship means that when graphed, the line will pass through the origin and be a straight line.

Thus, the correct answer is:
- **The relationship is proportional.**

Would you like more details or have any further questions?

Here are 5 related questions:
1. What is a proportional relationship in mathematics?
2. How can you graph a proportional relationship?
3. What happens to the graph if a relationship is non-proportional?
4. How do you find the constant of proportionality from a table?
5. How does time affect calorie burn in this context?

**Tip:** When checking for proportionality, always verify if the ratio between the variables stays consistent across all data points.

The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.

This problem explores whether the relationship between walking time (in minutes) and calories burned is proportional. The solution involves calculating the ratio for each data point and verifying if the ratio remains constant. This question is suitable for students in Grades 6-8.

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