To find the constant of proportionality from the provided data, we can analyze the relationship between the hours walked and the miles walked.
From the table, we have the following pairs:
- (14 hours, 1 mile)
- (12 hours, 2 miles)
- (34 hours, 3 miles)
- (1 hour, 4 miles)
Let's calculate the ratio of miles to hours for each pair:
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For (14 hours, 1 mile): \[ \text{Ratio} = \frac{1 \text{ mile}}{14 \text{ hours}} = \frac{1}{14} \]
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For (12 hours, 2 miles): \[ \text{Ratio} = \frac{2 \text{ miles}}{12 \text{ hours}} = \frac{1}{6} \]
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For (34 hours, 3 miles): \[ \text{Ratio} = \frac{3 \text{ miles}}{34 \text{ hours}} \approx \frac{1}{11.33} \]
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For (1 hour, 4 miles): \[ \text{Ratio} = \frac{4 \text{ miles}}{1 \text{ hour}} = 4 \]
The ratios of miles to hours do not show a constant value; thus it is not directly proportional in the traditional sense. However, we can still identify the constant of proportionality in the table from the pairs:
The pairs contain values:
- (14, 1) where 1 mile corresponds to 14 hours
- (12, 2) where 2 miles corresponds to 12 hours
- (34, 3) where 3 miles corresponds to 34 hours
- (1, 4) where 4 miles corresponds to 1 hour
Among the responses provided, the ratio that can be identified as a form of the constant of proportionality is:
- (14, 1) represents the relationship in hours and miles.
Thus, the answer is:
(14, 1).