To identify the constant of proportionality from the provided distances and times, we need to look at how many miles are walked per hour.
From the data given in the table, we can analyze the ratios:
-
For the first entry (14 hours, 1 mile):
- Ratio: \( \frac{1 \text{ mile}}{14 \text{ hours}} = \frac{1}{14} \)
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For the second entry (12 hours, 2 miles):
- Ratio: \( \frac{2 \text{ miles}}{12 \text{ hours}} = \frac{1}{6} \)
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For the third entry (34 hours, 3 miles):
- Ratio: \( \frac{3 \text{ miles}}{34 \text{ hours}} \)
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For the fourth entry (1 hour, 4 miles):
- Ratio: \( \frac{4 \text{ miles}}{1 \text{ hour}} = 4 \)
The constant of proportionality is represented by the ratio of miles to hours, expressed as miles per hour. In this case, the ratio that appears in the choices provided is:
- \((1, 4)\), which can be interpreted as "4 miles in 1 hour".
Thus, the best answer from the options for the constant of proportionality is:
(1, 4).