Final answer:
When two variables are inversely proportional, as one variable increases, the other variable decreases in the same proportion. By plugging in the given values into the inverse variation equation, we can find the constant of proportionality and solve for the unknown variable.
Step-by-step explanation:
When two variables are inversely proportional, it means that when one variable increases, the other variable decreases in the same proportion. Mathematically, this can be represented as y = k/x, where k is a constant.
In this case, we are given that y is -(1/4) when x is 8. Plugging these values into the equation, we have -(1/4) = k/8. Solving for k, we find that k = -2.
Now, we can use the value of k to find x when y is -(1/3). Substituting these values into the equation, we have -(1/3) = -2/x. Solving for x, we find that x = 6.