The value of z varies inversely with the value of w. the constant of variation is 2/3. which are possible values for z and w? check all that apply.

I can give you several pair of values that are possible and explain how to find them, such that you can apply the same to your options and choose the right ones.

The fact that z and w are inversely related means that their product is constant, this is:

v * w = constant.

The statement tells that the value ot the constant is 2/3, then:

v * w = 2/3

Now, you can solve for any of the variables and get:

v = (2/3) / w or w = (2/3) / v

Here are some values that meet that relation:

   v         w = (2/3) / v

-8/9        (2/3) / (-8/9) = - (2/3) * (9/8) = -3/4

- 4/9       (2/3) / (-4/9) = - (2/3) * (9/4) = - 3/2

- 2/9       (2/3) / (-2/9) = - (2/3) * (9/2) = - 3

2/9          (2/3) / ( 2/9) = (2/3) * (9/2) = 3

4/9          (2/3) / (4/9) = (2/3) * (9/4) = 3/2

What exactly is your question?