To find the constant of proportionality in Julian's walking situation, we can use the data provided in the scenario. Julian walks 2 miles in \(1/2\) hour.
To express the constant of proportionality, we can determine the ratio of distance walked to the time taken:
\[ \text{Distance} = 2 \text{ miles} \]
\[ \text{Time} = \frac{1}{2} \text{ hour} \]
The constant of proportionality is given by the ratio of distance to time:
\[ \text{Constant of Proportionality} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{\frac{1}{2} \text{ hour}} = 2 \div \frac{1}{2} = 2 \times 2 = 4 \text{ miles per hour} \]
Now, looking at the response choices, each option presents a ratio. Since the constant of proportionality we calculated is 4 (interpreted as 4 miles per hour), it's implied to look at it as a ratio such that it matches to the options given.
The closest match to 4 miles per hour expressed in the format of (time, distance) would be:
\[ (1, 4) \]
So, the constant of proportionality appears in the ratio (1, 4).
Final Answer: (1, 4)
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