Use the table to answer the question.
Time (hours) Pages read
12 15
1 30
112 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?
(1 point)
Responses
(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
The constant of proportionality can be found by looking at any pair of values (time, pages read) from the table.
For example, we can choose the pair (1, 30).
To find the ratio of the constant of proportionality, we divide the number of pages read by the time:
constant of proportionality = pages read / time = 30 / 1 = 30.
Therefore, the ratio of the constant of proportionality is:
(1, 30)
From the table provided, we can see that when Ruth reads for 1 hour, she reads 30 pages.
So the ratio of pages read to time in hours is (1, 30).
The correct answer is:
(1, 30)
To determine the constant of proportionality from the given table, we need to find a ratio that is the same for all pairs of values. In this case, we can compare the number of pages read to the time taken in hours.
Looking at the table, we see that as the time increases, the number of pages read also increases. We can compare different pairs of values to find the ratio. Let's try a few options:
(112, 30): The ratio here would be 112/30 = 3.73
(2, 60): The ratio here would be 2/60 = 0.03
(1, 30): The ratio here would be 1/30 = 0.033
(15, 12): The ratio here would be 15/12 = 1.25
From these options, we can see that the ratio that remains constant is (1, 30) with a ratio of 1/30 = 0.033.
So, the correct answer is (1, 30) - left parenthesis 1 comma 30 right parenthesis.