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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 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)

(4, 1)

(1, 4)

(1, 1/4)

1 answer

To find the constant of proportionality in the given table, we need to look at the relationship between the hours walked and the miles walked.

The constant of proportionality can be determined by the ratio of miles to hours in the table:

  1. For 1/4 hours, the ratio is 1 mile / (1/4 hour) = 1 / (1/4) = 4.
  2. For 1/2 hours, the ratio is 2 miles / (1/2 hour) = 2 / (1/2) = 4.
  3. For 3/4 hours, the ratio is 3 miles / (3/4 hour) = 3 / (3/4) = 4.
  4. For 1 hour, the ratio is 4 miles / 1 hour = 4 / 1 = 4.

In all cases, the constant of proportionality, which represents the number of miles walked per hour, is 4.

Given the options, the ratio that corresponds to this constant of proportionality is:

(4, 1)

So the correct response is (4, 1).