To determine if the relationship between time walking (minutes) and calories burned is proportional, we need to see if there is a constant ratio between the two quantities. A proportional relationship will have a straight line that passes through the origin (0,0) on a graph.
Let's calculate the ratios of calories burned to time walking for the given points:
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For 20 minutes: \[ \text{Ratio} = \frac{100 \text{ calories}}{20 \text{ minutes}} = 5 \]
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For 30 minutes: \[ \text{Ratio} = \frac{150 \text{ calories}}{30 \text{ minutes}} = 5 \]
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For 40 minutes: \[ \text{Ratio} = \frac{200 \text{ calories}}{40 \text{ minutes}} = 5 \]
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For 60 minutes: \[ \text{Ratio} = \frac{300 \text{ calories}}{60 \text{ minutes}} = 5 \]
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For 80 minutes: \[ \text{Ratio} = \frac{400 \text{ calories}}{80 \text{ minutes}} = 5 \]
Since the ratios are all the same (5), this indicates that there is a constant rate of calories burned per minute of walking.
However, to determine if it is proportional in the sense required, we notice there is no data point for 0 minutes, which means that the relationship does not start from the origin.
Therefore, the correct response is:
The relationship is non-proportional; the graph does not pass through the origin.
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