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