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
(14, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(1, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 4)
The answer is (1, 4) because the ratio between the hours and miles walked is consistent at 1 mile walked for every 4 hours.
To find the ratio at which the constant of proportionality appears, we need to look for a consistent ratio between the hours and the miles walked.
Looking at the table, we can see that for each hour, the number of miles walked follows a pattern.
When Julian walks for 14 hours, he walks 1 mile. This can be written as (14, 1).
However, if we examine the other entries in the table, we notice that the ratio between the hours and the miles walked is consistent at 12:2, 34:3, and 1:4.
Therefore, the ratio at which the constant of proportionality appears is (1, 4).
To find the constant of proportionality, we need to identify the ratio of miles walked to hours taken for each set of data in the table. Let's calculate the ratios for each data point:
For the first data point (14, 1), the ratio of miles walked to hours taken is 1/14.
For the second data point (12, 2), the ratio of miles walked to hours taken is 2/12, which simplifies to 1/6.
For the third data point (34, 3), the ratio of miles walked to hours taken is 3/34, which doesn't simplify any further.
For the fourth data point (1, 4), the ratio of miles walked to hours taken is 4/1, which simplifies to 4.
Now we can see that out of the given options, only one ratio appears as a constant throughout the table. That ratio is (4, 1). Therefore, the constant of proportionality appears at the ratio (4, 1).