Is the relationship between the variables inthe table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation write a function to model it
x: 2, 5, 12, 20
y: 30, 12, 5, 3
A. Direct variation: y = 15x
B. Inverse operation: y = 60/x
C. Direct variation: y = 2x + 2
D. Neither
I said neither because it doesn't seem to have a pattern at all.
I submitted it, it was right.
Oh so is y = 60/x correct?
Because 60/2 is 30, 60/5 is 12, 60/12 is 5, and 60/20 is 3
So that would fit x: 2, 5, 12, 20, y: 30, 12, 5, 3
It does have a pattern. Divide 60 by x
60 / 2 = 30
60 / 5 = 12
60 / 12 = 5
60 / 20 = 3
Therefore the correct answer is B) 60/x
As one increases, the other decreases. What does that tell you? Check by inserting x to find values of y
Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation write a function to model it
2 5 15 20
20 15 2 2
The relationship between the variables is an inverse variation because as one variable increases, the other variable decreases. The function that models this is:
y = 30/x
To determine if the relationship between the variables is a direct variation, an inverse variation, both, or neither, we can examine the pattern between the numbers in the table.
For direct variation, the ratio between the corresponding values of x and y should always be the same. This means that if we divide each y-value by its corresponding x-value, we should get a constant.
Let's check:
30 / 2 = 15
12 / 5 = 2.4
5 / 12 = 0.4167
3 / 20 = 0.15
As we can see, the ratios are not the same for all the pairs of values. Therefore, we can conclude that the relationship in the table is not a direct variation.
For inverse variation, the product of the corresponding values of x and y should always be the same. This means that if we multiply each x-value by its corresponding y-value, we should get a constant.
Let's check:
2 * 30 = 60
5 * 12 = 60
12 * 5 = 60
20 * 3 = 60
The product is the same for all the pairs of values, which indicates an inverse variation. Therefore, we can confirm that the relationship in the table is an inverse variation.
To write a function that models this inverse variation, we can use the form y = k/x, where k is the constant of variation. To find the value of k, we can substitute any pair of values from the table into the equation and solve for k.
Using the pair (2, 30):
30 = k / 2
30 * 2 = k
k = 60
Therefore, the function that models the inverse variation is:
y = 60/x
So, the correct answer is B. Inverse variation: y = 60/x.