Question

Find the constant of variation and write down the equation of variation.

Given data:

x = 2, 4, 6, 8
y = 36, 18, 12, 9


a. The constant of variation is 4.5 and the equation of variation is y = 4.5x.
b. The constant of variation is 9 and the equation of variation is y = 9x.
c. The constant of variation is 2 and the equation of variation is y = 2x.
d. The constant of variation is 6 and the equation of variation is y = 6x.

Answer 1

The student provided options do not contain the correct constant of variation or equation of variation. The constant of variation is 72 and the correct equation of variation is y = 72/x.

Step-by-step explanation:

The student has asked for help with finding the constant of variation and the equation of variation given a set of x and y values. To find the constant of variation, which is essentially the ratio of y to x, we can observe how y changes as x increases. When x = 2, y = 36, so our initial constant of variation is 36/2 = 18. Testing with the other values, when x = 4, y = 18; y/x = 18/4 = 4.5, showing us that the ratio is not constant across all values. However, we notice a pattern that each y is a result of 72 divided by x. Therefore, y varies inversely with x, and the constant of variation is 72.

The equation of variation where y is inversely proportional to x is y = k/x, where k is the constant of variation. Here, k = 72, so the equation of variation is y = 72/x.

The correct answer is not listed among the options provided by the student.