Question

Is the relationship between the variables a direct variation, an inverse variation or neither? If there is a variation write the function rule, where x is 2,3,4,5 y = 9,6,4.5,3.6

Answer 1

Indirect variation

Rule:
`y = (18)/(x)`

Explanation:

Given

`x \to 2,3,4,5`

`y \to 9,6,4.5,3.6`

Required

Determine the type of variation

For direct variation, we have:

y increases, as x increases

In the above function, y decreases, as x increases

Hence, it is not a direct variation

Indirect variation.

In an indirect variation, y decreases, as x increases

And the equation is given as:

`y = (k)/(x)`

Make k the subject

`k =xy`

Where k is the constant of variation.

For:

`(x,y) = (2,9)`

`k = 2 * 9 = 18`

For:

`(x,y) = (3,6)`

`k = 3 * 6 = 18`

For every other values;

`k = x * y = 18`

Hence, it is an indirect variation.

The rule is:

`y = (k)/(x)`

Substitute 18 for k

`y = (18)/(x)`