Question

Find the constant of proportionality for the following data set. Show your work.

Data set: (x, y)
(2, 4)
(5, 10)
(8, 16)

A. 2
B. 1
C. 0.5
D. 0.25

Answer 1

The correct answer is A.

k = 4/2 = 2

Answer 2

The constant of proportionality for the given data set is 2, as each y is twice its corresponding x, indicating that the values are directly proportional. The correct option is A.

Step-by-step explanation:

To find the constant of proportionality from the given data set, which represents pairs of values (x, y), we need to verify that y changes by the same multiple that x changes. This means that the relationship between x and y should be directly proportional, fitting the equation y = kx, where k is the constant of proportionality.

Let's check the given pairs (2, 4), (5, 10), and (8, 16):

• For (2, 4): k = y/x = 4/2 = 2
• For (5, 10): k = y/x = 10/5 = 2
• For (8, 16): k = y/x = 16/8 = 2

As we can see, the constant of proportionality (k) is the same in all cases, which confirms that the values are directly proportional with a constant of proportionality of 2. This corresponds to option A.