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
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(15, 1/2)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
(2, 60)
The correct answer is (1, 30)
To find the constant of proportionality, we need to determine the ratio between the number of pages read and the corresponding time.
Looking at the table, we can see that when Ruth reads 15 pages, it takes her 30 minutes. This can be represented as the ratio (15, 30).
So, the correct answer is:
(15, 30) or (15, 1/2)
To determine the ratio of the constant of proportionality, we can look for a pattern in the table. The constant of proportionality represents the relationship between the number of hours and the number of pages read.
From the data provided, we can observe that as the number of hours increases, the number of pages read also increases.
Looking at the table, we can see that for every 1 hour (12, 1, 2), the number of pages read increases by a consistent amount.
If we calculate the increase in pages read for each hour, we can find the ratio of the constant of proportionality.
- Increase from 12 to 1: Pages read increased by 30 - 15 = 15
- Increase from 1 to 2: Pages read increased by 60 - 30 = 30
Now we can calculate the ratio of the constant of proportionality by comparing the increase in pages read to the increase in hours:
- Increase from 12 to 1: 15 pages / 1 hour = 15/1 = 15
- Increase from 1 to 2: 30 pages / 1 hour = 30/1 = 30
From the calculations, we can see that the ratio of the constant of proportionality is 15 pages per hour.
Therefore, the correct answer is:
(15, 1/2) which represents the ratio of 15 pages per hour.