If $y$ varies directly as $x$, and if $y=8$ when $x=4$, the value of $y$ when $x=-8$ is:
$\textbf{(A)}\ -16 \qquad \textbf{(B)}\ -4 \qquad \textbf{(C)}\ -2 \qquad \textbf{(D)}\ 4k, k= \pm1, \pm2, \dots \qquad \\ \textbf{(E)}\ 16k, k=\pm1,\pm2,\dots$
If $y$ varies directly as $x$, then $\frac{x}{y}$ will be a constant for every pair of $(x, y)$.  Thus, we have:
$\frac{4}{8} = \frac{-8}{y}$
$y \cdot \frac{1}{2} = -8$
$y = -16$
$\boxed{\textbf{(A)}}$