Time (hours)%09Pages read%0D%0A12 %0915%0D%0A1%0930%0D%0A112 %0945%0D%0A2%0960%0D%0ARuth 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?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(2, 60)%0D%0Aleft parenthesis 2 comma 60 right parenthesis%0D%0A%0D%0A(1, 30)%0D%0Aleft parenthesis 1 comma 30 right parenthesis%0D%0A%0D%0A(15, 12)%0D%0Aleft parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis%0D%0A%0D%0A(112, 30)
From the data provided, the ratio of the constant of proportionality is (1, 30).
To find the ratio of the constant of proportionality, we need to compare the number of pages read to the corresponding time in hours.
Looking at the data provided, the best values to compare are:
(1, 30) - This represents the time in hours (1) and the corresponding number of pages read (30).
(2, 60) - This represents the time in hours (2) and the corresponding number of pages read (60).
To simplify the ratio, we divide both values by the greatest common divisor. In this case, both values can be divided by 30.
Dividing (1, 30) by 30, we get a ratio of (1/30, 1).
Dividing (2, 60) by 30, we get a ratio of (2/30, 2).
So, the ratio of the constant of proportionality is (1/30, 1) or in simplified form (1, 1).
To find the ratio of the constant of proportionality, we need to analyze the relationship between time (in hours) and pages read.
From the given data, we have:
Time (hours) | Pages read
-------------------------
12 | 15
1 | 30
112 | 45
2 | 60
To find the ratio, we can choose any two sets of values and calculate the ratio between the corresponding quantities. Let's choose the pair (1, 30) and (2, 60), representing the time and pages read after 1 hour and 2 hours, respectively.
For the pair (1, 30):
The ratio is calculated by dividing the pages read by the time, so the ratio is 30 pages / 1 hour = 30 pages/hour.
For the pair (2, 60):
The ratio is calculated by dividing the pages read by the time, so the ratio is 60 pages / 2 hours = 30 pages/hour.
As we can see, both pairs give us the same ratio of 30 pages/hour. Therefore, the constant of proportionality is 30 pages/hour.
So, the correct option is: (1, 30)