To determine the constant of proportionality in the relationship between hours walked and miles walked, we can find the ratio of miles walked to hours at any point in the table.
The data you've provided is:
- (1/4, 1)
- (1/2, 2)
- (3/4, 3)
- (1, 4)
We can calculate the ratio of miles to hours for each pair:
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For (1/4, 1): \[ \text{Ratio} = \frac{1 \text{ mile}}{1/4 \text{ hour}} = \frac{1}{1/4} = 4 \]
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For (1/2, 2): \[ \text{Ratio} = \frac{2 \text{ miles}}{1/2 \text{ hour}} = \frac{2}{1/2} = 4 \]
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For (3/4, 3): \[ \text{Ratio} = \frac{3 \text{ miles}}{3/4 \text{ hour}} = \frac{3}{3/4} = 4 \]
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For (1, 4): \[ \text{Ratio} = \frac{4 \text{ miles}}{1 \text{ hour}} = \frac{4}{1} = 4 \]
In all cases, the ratio of miles to hours is constant and equals 4. This means that for every hour of walking, Julian walks 4 miles.
Now, looking at the answer choices you've given:
A. (1/4, 1)
B. (4, 1)
C. (1, 1/4)
D. (1, 4)
Since the constant ratio of miles to hours is 4 miles per hour, the correct answer where this ratio appears is:
D. (1, 4)
This indicates that in 1 hour, Julian walks 4 miles.