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, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(14, 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
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The constant of proportionality appears at the ratio of (1, 4).
To determine the ratio at which the constant of proportionality appears, we need to compare the hours and miles walked in the table. Looking at the table, we see that the constant ratio between the hours and miles walked is 1 hour to 2 miles. Therefore, the correct option is:
(1, 4)
left parenthesis 1 comma 4 right parenthesis
To determine the ratio at which the constant of proportionality appears, we need to examine the relationship between the hours and miles walked in the table.
The table shows the number of hours it takes Julian to walk a certain number of miles. Looking at the data, we can see that as the number of miles walked increases, the number of hours also increases.
Let's calculate the proportional values for the table:
For the first row (14, 1), we can calculate the ratio as 1/14 ≈ 0.0714.
For the second row (12, 2), the ratio is 2/12 = 1/6 ≈ 0.1667.
For the third row (34, 3), the ratio is 3/34 ≈ 0.0882.
For the fourth row (1, 4), the ratio is 4/1 = 4.
From these calculations, we can determine that the constant of proportionality appears at the ratio of 1/4, which is given by the option (1, 4) in the question:
(1, 4)
left parenthesis 1 comma 4 right parenthesis