Proportional Relationships in Tables Quick Check

1 of 51 of 5 Items
Question
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

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

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

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

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

To find the constant of proportionality, we want to look for the ratio of miles walked to hours. We can calculate the constant of proportionality (k) by dividing the number of miles by the number of hours for any point in the table.

Let's look at the entries in the table:

  1. For the entry (14 hours, 1 mile): \[ \text{Constant of proportionality } (k) = \frac{1}{14} \]

  2. For the entry (12 hours, 2 miles): \[ k = \frac{2}{12} = \frac{1}{6} \]

  3. For the entry (34 hours, 3 miles): \[ k = \frac{3}{34} \]

  4. For the entry (1 hour, 4 miles): \[ k = \frac{4}{1} = 4 \]

All the ratios do not yield the same constant of proportionality, which suggests that the values in the table may not be proportional. However, to answer your question about which ratio reflects the constant of proportionality, the most appropriate one based on how the table is structured is the ratio of (1 mile : 14 hours), which corresponds to \( \left(1, \frac{1}{14}\right) \).

Thus, the correct response that matches the constant of proportionality (the ratio of miles to hours, \( \frac{miles}{hours} \)) from the options presented would be:

(1, 14).

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