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Use the table to answer the question.

Hours - Miles walked
1/4 - 1
1/2 - 2
3/4 - 3
1 - 4
It takes Julian 12 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)

(4, 1)

(1, 1/4)

(1, 4)

1 answer

To find the constant of proportionality in the data table, we look for the ratio of hours to miles walked.

From the table:

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

The constant of proportionality is 4, meaning for every hour, Julian walks 4 miles.

Looking at the response options, the ratio (4, 1) reflects this constant of proportionality.

Therefore, the answer is:

(4, 1)