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 (1, 14) left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis (1, 4) left parenthesis 1 comma 4 right parenthesis (14, 1)
The ratio at which the constant of proportionality appears is (1, 4), which means for every 1 hour, Julian walks 4 miles.
The constant of proportionality appears at the ratio (1, 4), which means that for every 1 hour Julian walks, he covers a distance of 4 miles.
To find the constant of proportionality in this table, we need to calculate the ratios between the hours and miles walked. The constant of proportionality is the value that remains the same in each ratio.
Let's calculate the ratios for each data point in the table:
For the first row, the ratio is 1 mile walked in 14 hours (1:14).
For the second row, the ratio is 2 miles walked in 12 hours (2:12), which simplifies to 1:6.
For the third row, the ratio is 3 miles walked in 34 hours (3:34), which simplifies to approximately 1:11.33.
For the fourth row, the ratio is 4 miles walked in 1 hour (4:1) or 4:1.
Looking at the ratios, we can see that the ratio (1,4) appears to have a constant value of 1. Every time we increase the number of miles walked, the number of hours decreases by the same factor of 4. This means the constant of proportionality is 1:4.
Therefore, the correct answer is (1, 4) - the ratio (1,4) indicates the constant of proportionality in this table.