Determine whether y varies directly with x. If​ so, find the constant of variation and write the function rule.

Question

x
18
60
63
y
6
20
21

What is the constant of​ variation? Select the correct choice and fill in any answer boxes in your choice below.

A.
k=
  
enter your response here ​(Simplify your answer. Type an integer or a​ fraction.)
B.
There is no constant of variation.

Answer 1

To determine if y varies directly with x, we can check if the ratio of y to x remains constant.

For the first pair, y = 6 and x = 18, the ratio is 6/18 = 1/3.
For the second pair, y = 20 and x = 60, the ratio is 20/60 = 1/3.
For the third pair, y = 21 and x = 63, the ratio is 21/63 = 1/3.

Since the ratio of y to x is always 1/3, we can conclude that y varies directly with x.

To find the constant of variation (k), we can use any of the pairs. Let's use the second pair of values:

k = y/x = 20/60 = 1/3

Therefore, the constant of variation is 1/3.

The function rule for this direct variation is: y = (1/3)x.