The table below shows the number of color pages a printer prints out over a period of time.
Printed Pages in Color
Time (min), x
2
6
8
18
Number of pages, y
3
9
12
27
What is the constant of variation?
Two-thirds
Three-halves
2
3
To find the constant of variation, we need to determine the relationship between the two variables, time (min) and number of pages (y).
Using the given data, we can observe that as the time increases, the number of pages printed in color also increases.
Let's calculate the ratios of y to x for each data point:
- For the first data point (2 min, 3 pages): 3 / 2 = 1.5
- For the second data point (6 min, 9 pages): 9 / 6 = 1.5
- For the third data point (8 min, 12 pages): 12 / 8 = 1.5
- For the fourth data point (18 min, 27 pages): 27 / 18 = 1.5
The ratios are all equal to 1.5. Therefore, the constant of variation is 1.5.
Answer: Three-halves
To find the constant of variation, we need to calculate the ratio of the number of pages (y) to the time (x) for each data point.
Calculating the ratios:
- For the first data point: y/x = 3/2 = 1.5
- For the second data point: y/x = 9/6 = 1.5
- For the third data point: y/x = 12/8 = 1.5
- For the fourth data point: y/x = 27/18 = 1.5
Since the ratios are consistent and equal to 1.5, the constant of variation is 1.5.
Therefore, the correct answer is Three-halves.