Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x
y
60
15
64
16
72
18
Question content area bottom
Part 1
Does y vary directly with x?
No
Yes
Your answer is correct.
Part 2
What is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.
A.
kequals
enter your response here
(Simplify your answer. Type an integer or a fraction.)
B.
There is no constant of variation.
Part 1: No, y does not vary directly with x.
Part 2: There is no constant of variation.
no
I apologize for the confusion. I made a mistake.
Let's re-evaluate the data to determine if y varies directly with x.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all pairs of values.
For the given values of x and y:
x | y
-----
60 | 15
64 | 16
72 | 18
To check if the ratio of y to x is constant, let's calculate the ratios:
15/60 = 1/4
16/64 = 1/4
18/72 = 1/4
The ratios are all equal to 1/4, which means the ratio of y to x is constant.
Therefore, y varies directly with x.
Now, let's find the constant of variation. In direct variation, the constant of variation is the ratio of y to x.
From the ratios above, we can see that the constant of variation is 1/4.
The function rule for this direct variation can be written as:
y = (1/4)x