Question 134911
This question is asking for the EQUATION and thus it is NOT asking you to solve for any letters in particular.

If z varies jointly as y and the cube of x, then we have this equation:

z = k(x^3)(y), where k is the constant of variation.

Let plug the given numbers WITHOUT solving for k.

160 = k(2)^3(-5)

160 = k(8)(-5)

160 = -40k

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You said:

"I was looking for: y=-4xy^3, y=4x^3y, y=4xy^3, y=-4x^3y"

I said:
 
In the question, you did not indicate that the constant of variation, which is k needed to be found.
 
I found this equation:
 
160 = -40k
 
Divide both sides by -40 and k = -4.
 
Then your equation and answer is:
 
z = -4x^3y 
 
It cannot be y = -4x^3y because z varies jointly as y and the cube of x.
 
In other words, if your question has a letter z, then z MUST appear or be part of your equation.