Use the table to answer the question.
Hours Miles walked
14 1
12 2
34 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)
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
(1/4, 1)
The constant of proportionality appears at the ratio (1/4, 1).
To determine the ratio at which the constant of proportionality appears, we need to compare the number of miles walked to the time taken in each instance. The ratio would be the miles walked divided by the time taken. Let's calculate the ratio for each set of data:
For the first set (14 hours, 1 mile):
Ratio = 1 mile / 14 hours = 1/14
For the second set (12 hours, 2 miles):
Ratio = 2 miles / 12 hours = 1/6
For the third set (34 hours, 3 miles):
Ratio = 3 miles / 34 hours = 3/34
For the fourth set (1 hour, 4 miles):
Ratio = 4 miles / 1 hour = 4/1
From the calculations, the only set of data that has a constant ratio (or constant of proportionality) is the fourth set: (1 hour, 4 miles), represented by the ratio 4/1.
Therefore, the correct answer is (4, 1).
To find the constant of proportionality in the given data table, we need to compare the hours and miles walked for each pair of values.
Let's calculate the ratios for each pair:
For the first pair (14 hours, 1 mile), the ratio is 1/14 (1 mile walked in 14 hours).
For the second pair (12 hours, 2 miles), the ratio is 2/12 (2 miles walked in 12 hours).
For the third pair (34 hours, 3 miles), the ratio is 3/34 (3 miles walked in 34 hours).
For the fourth pair (1 hour, 4 miles), the ratio is 4/1 (4 miles walked in 1 hour).
Out of these ratios, the only option that represents the constant of proportionality is (4, 1). This means that for every 4 miles walked, it takes 1 hour.
So, the correct answer is (4, 1) or "left parenthesis 4 comma 1 right parenthesis."