Hours Miles walked
1/4 1
1/2 2
3/4 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, 1/4)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(1/4, 1)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
To find the constant of proportionality in the given data, we need to determine the ratio of miles walked to the time taken to walk that distance for each pair of values.
Let's calculate the ratios for each pair:
For the first pair (1/4 hour, 1 mile), the ratio is 1/4 / 1 = 1/4.
For the second pair (1/2 hour, 2 miles), the ratio is 2 / 1/2 = 4.
For the third pair (3/4 hour, 3 miles), the ratio is 3 / 3/4 = 4.
For the fourth pair (1 hour, 4 miles), the ratio is 4 / 1 = 4.
Now, let's see which ratio appears as a constant in all the pairs:
1/4, 4, 4, 4
We can see that the ratio 4 appears as a constant in all pairs. So, the constant of proportionality is 4.
Therefore, the correct answer is (4, 1), or "left parenthesis 4 comma 1 right parenthesis."