Use the table to answer the question.

Question

Hours Miles walked
1/4 1
1/2 2
3/4 3
1 4
It takes Julian 1/2 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 of proportionality appear

Answer 1

To determine the constant of proportionality based on the data provided in the table, we can look at the relationship between hours walked and miles walked. The constant of proportionality (k) can be found using the formula:

\[ k = \frac{\text{Miles walked}}{\text{Hours walked}} \]

We can calculate this for each entry in the table:

1. For \( \frac{1}{4} \) hours: \[ k = \frac{1}{\frac{1}{4}} = 4 \]

2. For \( \frac{1}{2} \) hours: \[ k = \frac{2}{\frac{1}{2}} = 4 \]

3. For \( \frac{3}{4} \) hours: \[ k = \frac{3}{\frac{3}{4}} = 4 \]

4. For \( 1 \) hour: \[ k = \frac{4}{1} = 4 \]

In each case, the constant of proportionality is \( k = 4 \). This means that for every hour walked, Julian covers 4 miles.

Thus, the constant of proportionality appears to be 4.