Use the table to answer the 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?

(1 point)
Responses

(1/4, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(1, 4)
left parenthesis 1 comma 4 right parenthesis

(1, 1/4)

1 answer

To find the constant of proportionality from the table, we look for the ratio of miles walked to hours. The constant of proportionality can be found by dividing miles by hours for any entry in the table.

Using the data in the table:

  • For \( (1/4, 1) \): \( \frac{1}{1/4} = 4 \)
  • For \( (1/2, 2) \): \( \frac{2}{1/2} = 4 \)
  • For \( (3/4, 3) \): \( \frac{3}{3/4} = 4 \)
  • For \( (1, 4) \): \( \frac{4}{1} = 4 \)

In each case, the constant of proportionality is \( 4 \), indicating that Julian walks \( 4 \) miles for every hour he spends walking.

Looking at the response options provided, the ratio that matches the constant of proportionality appears as:

(4, 1)

So the correct answer is:

(4, 1).