To find the constant of proportionality in Julian's data, we can use the ratio of miles walked to hours taken.
From the data table:
-
For \( \left(\frac{1}{4}, 1\right) \):
The ratio is \( \frac{1}{\frac{1}{4}} = 4 \). -
For \( \left(\frac{1}{2}, 2\right) \):
The ratio is \( \frac{2}{\frac{1}{2}} = 4 \). -
For \( \left(\frac{3}{4}, 3\right) \):
The ratio is \( \frac{3}{\frac{3}{4}} = 4 \). -
For \( (1, 4) \):
The ratio is \( \frac{4}{1} = 4 \).
In every case, the constant of proportionality is 4.
Looking through the options provided:
- (1/4, 1) → This does not represent the ratio of miles to hours.
- (1, 4) → This indicates a ratio, but in the format of hours to miles, it represents the point, not the ratio we are looking for.
- (4, 1) → This suggests a ratio of 4 miles for 1 hour.
- (1, 1/4) → This does not represent the correct ratio either.
The ratio that indicates the constant of proportionality from the data (which is 4 miles per hour) would be represented by the option \( (4, 1) \). This indicates 4 miles for every 1 hour.