Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x
27
30
57
y
9
10
19
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 need to check if the ratio between y and x remains constant.
For example, let's calculate the ratios for the given data points:
27/9 = 3
30/10 = 3
57/19 = 3
The ratios are all equal to 3. Therefore, y varies directly with x.
The constant of variation (k) can be found by taking any ratio:
k = y/x = 9/27 = 1/3
So, the constant of variation is 1/3.
The function rule for direct variation is y = kx. Thus, in this case, the function rule is y = (1/3)x.
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
A.
y=
enter your response here
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B.
There is no function rule.
The correct function rule is:
A. y = (1/3)x