Question

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

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

(1, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis

(14, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis

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

To find the constant of proportionality in the context of the given data, you need to look for a ratio that represents the relationship between hours walked and miles walked.

From the data in the table, we can extract the quantities:

1. (14 hours, 1 mile)
2. (12 hours, 2 miles)
3. (34 hours, 3 miles)
4. (1 hour, 4 miles)

To calculate the constant of proportionality, we can find the ratio of miles walked to hours spent walking. This can be computed as follows:

- For 14 hours and 1 mile: \( \frac{1}{14} \) miles per hour.
- For 12 hours and 2 miles: \( \frac{2}{12} = \frac{1}{6} \) miles per hour.
- For 34 hours and 3 miles: \( \frac{3}{34} \) miles per hour.
- For 1 hour and 4 miles: \( \frac{4}{1} = 4 \) miles per hour.

From this analysis, the constant of proportionality appears to be indicated by the last ratio calculation involving (1 hour, 4 miles), where the result is 4 miles per hour.

Therefore, the answer to your question regarding the ratio that represents the constant of proportionality is:

**(1, 4)**