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.
Calculating the ratio for each time increment:
- 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 walking is consistent and equals 5 for all data points, the relationship is indeed proportional.
However, to also consider the second part of the criteria for a proportional relationship: it must pass through the origin (0,0). In this case, the table does not provide data for 0 minutes; thus, we can't definitively conclude that it passes through the origin.
Based on this analysis, the best response is:
The relationship is non-proportional; the graph does not pass through the origin.
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