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 ratio at which the constant of proportionality appears is (12, 2).
To determine the ratio for the constant of proportionality, we can use the table provided. The ratio can be found by comparing the number of miles walked to the number of hours taken for each data point in the table.
We can look at the first row of the table: 1 mile walked in 14 hours.
The ratio for this data point would be (1, 14), which means 1 mile is walked in 14 hours.
Therefore, the correct option is (1, 14).
To determine at which ratio the constant of proportionality appears, we need to examine the relationship between the hours and miles walked.
From the table, we can see that as the number of hours increases, the number of miles walked also increases. This indicates that there is a direct relationship between the two variables.
To find the constant of proportionality, we can compare any pair of values from the table. Let's choose the pair (12, 2), where Julian took 12 hours to walk 2 miles.
To calculate the ratio between hours and miles, we divide the number of miles by the number of hours:
2 miles / 12 hours = 1/6
Therefore, the constant of proportionality in this case is 1/6.
Now, looking at the answer choices given:
(1, 14) does not represent the ratio of miles to hours.
(14, 1) does not represent the ratio of miles to hours.
(4, 1) does not represent the ratio of miles to hours.
(1, 4) represents the ratio of miles to hours as 1/4.
Therefore, the correct answer is (1, 4).