Question

Use the table to answer the question.

Number of Miles Walked Corresponding to the Number of Hours Spent Walking
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

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(1, 4)
left parenthesis 1 comma 4 right parenthesis

(1, 14)

Answer 1

To find the constant of proportionality, we can look at the ratio of miles walked to the hours spent walking from the table.
We need to calculate the ratio for each pair of values:

1. For \( (14, 1) \):
\[
\text{Ratio} = \frac{1}{14}
\]

2. For \( (12, 2) \):
\[
\text{Ratio} = \frac{2}{12} = \frac{1}{6}
\]

3. For \( (34, 3) \):
\[
\text{Ratio} = \frac{3}{34}
\]

4. For \( (1, 4) \):
\[
\text{Ratio} = \frac{4}{1} = 4
\]

From these calculations, the ratio that appears as the constant of proportionality can be taken from the pair \( (1, 4) \) since it reflects the proportional relationship of miles to hours, indicating that for every hour, he would walk 4 miles, which is consistent.

Thus, the correct answer is:

**(1, 4)**.