An equation typically used to represent inverse variation is y = k/x, where k is the "constant of proportionality for inverse variation."
6y = x does not represent inverse variation, since y increases when x increases or x increases when y increases. This is an example of direct proportion and is thus not an answer.
1/2y = 1/x should be written as (1/2)y = 1/x, to emphasize that (1/2) is a coefficient of y. Let's solve for y to see what form the resulting equation has:
(1/2)y = 1/x => y = 2/x. This has the form y = k/x, and thus represents inverse variation. y decreases when x increases.
–x = y + 8 is a linear equation and thus could not possibly represent inverse proportion. The "offset," +8, also makes it impossible for –x = y + 8 to represent direct variation. Reject this answer choice.
y = 1/4x has the form y = (1/4)x, which resembles a rule for direct variation.
Note, however, that if you really meant y = 1 / (4x), or y = (1/4)(1/x), then this would be a case of inverse variation.
The only answer choice in this problem that clearly represents indirect variation is (1/2)y = 1/x (as I have already said, above).
