Proportional Relationships in Tables Quick Check
2 of 52 of 5 Items

Question
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

(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis

(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)
(2, 60)
left parenthesis 2 comma 60 right parenthesis
To determine the ratio of the constant of proportionality from the data provided, we can compare the number of pages read to the corresponding time in hours.
Looking at the table, we can see that for every 1 hour (time) in the first row, Ruth reads 15 pages. If we think about it as a ratio, it would be (15, 1) since the number of pages is 15 and the time is 1 hour.
Therefore, the correct answer is: (15, 1)
To find the ratio of the constant of proportionality in a table, we need to compare the change in the dependent variable (pages read) to the change in the independent variable (time).
Looking at the table, we can see that as the time increases, the number of pages read also increases. Let's calculate the rate of change between each pair of points:
From (12, 15) to (1, 30):
Change in pages read = 30 - 15 = 15
Change in time = 1 - 12 = -11
Rate = change in pages read / change in time = 15 / (-11) = -15/11
From (1, 30) to (112, 45):
Change in pages read = 45 - 30 = 15
Change in time = 112 - 1 = 111
Rate = change in pages read / change in time = 15 / 111 = 5/37
From (112, 45) to (2, 60):
Change in pages read = 60 - 45 = 15
Change in time = 2 - 112 = -110
Rate = change in pages read / change in time = 15 / (-110) = -3/22
From these calculations, we can see that the rate of change is not constant. Therefore, there is no constant of proportionality in this data set. None of the given options is the correct answer.