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 (1, 4) left parenthesis 1 comma 4 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 (4, 1)
A. (1, 4)
B. (1, 1/4)
C. (1/4, 1)
D. (4,1)
The constant of proportionality appears at the ratio (1, 4).
Answer: A. (1, 4)
To determine the ratio at which the constant of proportionality appears in the table, we need to calculate the ratio of miles walked to the corresponding number of hours for each set of data.
For the first set of data, the ratio is 1 mile walked in 14 hours, which can be written as 1:14.
For the second set of data, the ratio is 2 miles walked in 12 hours, which can be simplified to 1:6.
For the third set of data, the ratio is 3 miles walked in 34 hours, which can be simplified to 3:34.
For the fourth set of data, the ratio is 4 miles walked in 1 hour, which can be written as 4:1.
From the ratios calculated above, we can see that the ratio (1, 4) represents the constant of proportionality.
Therefore, the correct answer is A. (1, 4).
To find the ratio at which the constant of proportionality appears, we need to look for a pattern in the table.
If we divide the miles walked by the number of hours, we can see if there is a constant value.
Let's calculate the ratios for each row in the table:
- For the first row, 1 mile walked divided by 14 hours is approximately 0.0714.
- For the second row, 2 miles walked divided by 12 hours is approximately 0.1667.
- For the third row, 3 miles walked divided by 34 hours is approximately 0.0882.
- For the fourth row, 4 miles walked divided by 1 hour is 4.
Looking at these ratios, we can see that the constant of proportionality appears at the ratio (1, 4). Therefore, the answer is A. (1, 4).