Use the table to answer the question.%0D%0A%0D%0AHours%09Miles walked%0D%0A14%0D%0A1%0D%0A4%0D%0A1%0D%0A12%0D%0A1%0D%0A2%0D%0A2%0D%0A34%0D%0A3%0D%0A4%0D%0A3%0D%0A1%094%0D%0AIt takes Julian 12%0D%0A1%0D%0A2%0D%0A 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?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(1, 4)%0D%0A(%0D%0A1%0D%0A,%0D%0A %0D%0A4%0D%0A)%0D%0Aleft parenthesis 1 comma 4 right parenthesis%0D%0A%0D%0A(4, 1)%0D%0A(%0D%0A4%0D%0A,%0D%0A %0D%0A1%0D%0A)%0D%0Aleft parenthesis 4 comma 1 right parenthesis%0D%0A%0D%0A(1, 14)%0D%0A(%0D%0A1%0D%0A,%0D%0A %0D%0A1%0D%0A4%0D%0A)%0D%0Aleft parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis%0D%0A%0D%0A(14, 1)

Answer 1

To determine the constant of proportionality in Julian's walking data, we need to find the ratio of miles walked to hours spent walking for each entry in the data table.

From the data provided, we can summarise it as follows:

1. 2 miles / 1 hour = 2 miles/hour
2. 4 miles / 1 hour = 4 miles/hour
3. 3 miles / 1 hour = 3 miles/hour
4. 4 miles / 1 hour = 4 miles/hour
5. 1 mile / 4 hours = 0.25 miles/hour

The ratios of miles to hours (miles/hour) from the selected entries above are:

• For (1, 2): ratio of 2
• For (1, 4): ratio of 4
• For (1, 3): ratio of 3

The most consistent ratio in terms of higher values is 4, which corresponds to the (4, 1) ratio where 4 miles are walked in 1 hour.

So the answer is:

(4, 1).