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
(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 correct answer is (1, 4).
To determine the ratio at which the constant of proportionality appears, we can calculate the ratio of miles walked to the corresponding number of hours for each row in the table:
For the first row: 1 mile / 14 hours = 1/14
For the second row: 2 miles / 12 hours = 2/12 = 1/6
For the third row: 3 miles / 34 hours = 3/34
For the fourth row: 4 miles / 1 hour = 4/1 = 4
Among these ratios, we can see that the ratio (1, 6) appears as the constant of proportionality.
To determine at which ratio the constant of proportionality appears in the table, we need to observe the relationship between the hours and the miles walked.
We can start by calculating the ratios of hours to miles walked for each row in the table:
For the first row (14 hours, 1 mile), the ratio is 14/1 = 14.
For the second row (12 hours, 2 miles), the ratio is 12/2 = 6.
For the third row (3 hours, 3 miles), the ratio is 3/3 = 1.
For the fourth row (1 hour, 4 miles), the ratio is 1/4 = 1/4.
From these ratios, we can see that the only ratio that remains constant (the constant of proportionality) is the ratio of 1/4 in the fourth row (1 hour, 4 miles). Therefore, the answer is:
(1, 4)
left parenthesis 1 comma 4 right parenthesis