The equation for an inverse variation:

\(\displaystyle{y}=\frac{{k}}{{x}}\)

Solve for k:

\(\displaystyle-\frac{{1}}{{4}}=\frac{{k}}{{-{8}}}\)

\(\displaystyle{k}={\left(-{8}\right)}\times{\left(-\frac{{1}}{{4}}\right)}\)

k=2

Substitute x=4, to find y:

\(\displaystyle{y}=\frac{{2}}{{4}}\)

\(\displaystyle{y}=\frac{{1}}{{2}}\)

\(\displaystyle{y}=\frac{{k}}{{x}}\)

Solve for k:

\(\displaystyle-\frac{{1}}{{4}}=\frac{{k}}{{-{8}}}\)

\(\displaystyle{k}={\left(-{8}\right)}\times{\left(-\frac{{1}}{{4}}\right)}\)

k=2

Substitute x=4, to find y:

\(\displaystyle{y}=\frac{{2}}{{4}}\)

\(\displaystyle{y}=\frac{{1}}{{2}}\)