Use the table to answer the question.
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 point)
Responses
(1/4, 1)
(4, 1)
(1, 1/4)
(1, 4)
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The constant of proportionality appears at the ratio (1, 4).
To determine at which ratio the constant of proportionality appears, we need to look for a consistent ratio between the hours and miles walked.
Let's compare the ratios of hours to miles walked:
- For the first row: 1/4 hour to walk 1 mile, the ratio is 1/4.
- For the second row: 1/2 hour to walk 2 miles, the ratio is 2/ (1/2) = 4.
- For the third row: 3/4 hour to walk 3 miles, the ratio is 3/ (3/4) = 4.
- For the fourth row: 1 hour to walk 4 miles, the ratio is 4/1 = 4.
From the table, we can see that the consistent ratio between the hours and miles walked is 4.
Therefore, the correct answer is (4, 1).
To find the ratio at which the constant of proportionality appears, we need to analyze the relationship between the hours and the miles walked in the table.
The constant of proportionality appears when the ratio between the hours and the miles walked remains the same. In other words, we are looking for a ratio that is consistent throughout the table.
Let's calculate the ratios for each row of the table:
For the first row: Ratio = (1/4) / 1 = 1/4
For the second row: Ratio = (1/2) / 2 = 1/4
For the third row: Ratio = (3/4) / 3 = 1/4
For the fourth row: Ratio = 1 / 4 = 1/4
As we can see, the ratio (1/4) is consistent throughout the table. Therefore, the constant of proportionality appears at the ratio (1/4, 1).
So the correct answer is (1/4, 1).