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 (2, 60) left parenthesis 2 comma 60 right parenthesis (15, 12) left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis (1, 30) left parenthesis 1 comma 30 right parenthesis (112, 30)
A. (2, 60)
B. (15. 1/2)
C. (1, 30)
D. (1 1/2, 30)
The correct answer is B. (15. 1/2).
To find the constant of proportionality, we need to find the ratio between the number of pages read and the time taken to read them.
From the table, we can see that when Ruth reads 15 pages, she takes 30 minutes.
So the ratio between the number of pages read and the time taken is 15:30, which simplifies to 1:2.
Therefore, the constant of proportionality is 1/2.
To determine the constant of proportionality, we can compare the ratio of pages read to the corresponding time in hours.
From the table, Ruth reads 15 pages in 30 minutes (which is equivalent to 0.5 hours). We can calculate this ratio by dividing the pages read by the time:
Ratio = Pages read / Time
For the given data point, the ratio is 15 pages / 0.5 hours, which simplifies to 30 pages/hour.
Therefore, the constant of proportionality is 30.
Among the given options, the correct answer is:
A. (2, 60)
To find the ratio of constant proportionality in a proportional relationship, we need to determine the ratio of the dependent variable (pages read) to the independent variable (time in hours).
Looking at the table, we can see that as time increases, the number of pages read also increases.
If we examine the rows:
- For the first row, when 12 pages are read in 1 hour, we can see that for every 12 pages read, it takes 1 hour. Therefore, the ratio is (12, 1).
- For the second row, when 15 pages are read in 30 minutes (which is equivalent to 0.5 hours), we can see that for every 15 pages read, it takes 0.5 hours. Therefore, the ratio is (15, 0.5).
Comparing the two ratios, we can simplify them to:
(12, 1) becomes (15, 0.5) because 1 hour is equivalent to 0.5 hours.
So, from the data provided, the ratio of the constant of proportionality is (15, 0.5), which can be written as (15, 1/2).
Therefore, the correct answer is B. (15, 1/2).