It takes Julian a half an hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance. He created the data table at which ratio does the constant proportionality appear.
To analyze the data and determine the constant proportionality, we need to examine the relationship between the time it takes Julian to walk and the distance he covers. From the given information, we know that Julian takes half an hour to walk 2 miles.
Let's create a data table to compare the time and distance Julian would cover:
| Time (in hours) | Distance (in miles) |
|-----------------|---------------------|
| 0.5 | 2 |
| 1 | 4 |
| 1.5 | 6 |
| 2 | 8 |
To find the constant proportionality, we can divide the distance by the time:
| Time (in hours) | Distance (in miles) | Distance / Time |
|-----------------|---------------------|-----------------|
| 0.5 | 2 | 4 |
| 1 | 4 | 4 |
| 1.5 | 6 | 4 |
| 2 | 8 | 4 |
As observed, the ratio between "Distance" and "Time" remains constant at 4. Therefore, the constant proportionality appears at a ratio of 4.