Use the table to answer the question.
Hours Miles walked
14 1
12 2
34 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)
left parenthesis 1 comma 4 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(14, 1)
The ratio at which the constant of proportionality appears is (14, 1).
To find the ratio of the constant of proportionality, we need to compare the values of hours and miles walked. Looking at the table, we can see that as the hours increase, the miles walked also increase.
The ratio of the constant of proportionality appears in the (1, 14) pair. This means that for every 1 hour, Julian walks 14 miles.
To find the constant of proportionality in the table, we need to determine the ratio between the number of hours and the number of miles walked. Let's calculate this ratio for each row of the table:
For the first row: 14 hours / 1 mile = 14/1 = 14
For the second row: 12 hours / 2 miles = 12/2 = 6
For the third row: 34 hours / 3 miles = 34/3 ≈ 11.33
For the fourth row: 1 hour / 4 miles = 1/4 = 0.25
From the calculations, we can see that the ratio between the hours and miles varies for each row. Therefore, the constant of proportionality does not appear in the given table. None of the given options (1, 4), (4, 1), (1, 14) or (14, 1) represents the correct ratio for the constant of proportionality.