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
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(14, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(4, 1)
The ratio at which the constant of proportionality appears is (1, 4)
To determine the ratio at which the constant of proportionality appears, we need to examine the relationship between the hours and miles walked. We can calculate the ratio by dividing the miles by the hours for each data point:
For the first data point (14, 1): 1 / 14 = 0.0714
For the second data point (12, 2): 2 / 12 = 0.1667
For the third data point (34, 3): 3 / 34 = 0.0882
For the fourth data point (1, 4): 4 / 1 = 4
Out of the given options, the only ratio that appears to be constant is the ratio (1, 4) which corresponds to the fourth data point. Therefore, the correct answer is:
(1, 4)
To determine the ratio at which the constant of proportionality appears, we need to look for a consistent ratio between the hours and the miles walked. In other words, we need to find a ratio that remains the same throughout the table.
Let's calculate the ratios for each pair of values given in the table:
Ratio for the first pair (14 hours, 1 mile): 14/1 = 14
Ratio for the second pair (12 hours, 2 miles): 12/2 = 6
Ratio for the third pair (34 hours, 3 miles): 34/3 ≈ 11.33
Ratio for the fourth pair (1 hour, 4 miles): 1/4 = 0.25
As we can see, the ratio that remains constant is the ratio of hours to miles walked of 1/4.
Therefore, the correct answer is (1, 4), which corresponds to the ratio (1 hour, 4 miles).