Answer
When $[H_3O^+]$ increases, $[OH^-]$ decreases.
When $[H_3O^+]$ decreases, $[OH^-]$ increases.
Work Step by Step
Looking at the $K_w$'s expression:
$[OH^-] * [H_3O^+] = K_w$
Isolating $[OH^-]$:
$[OH^-] = \frac{K_w}{[H_3O^+]}$
Since $K_w$ has a constant value, if we decrease $[H_3O^+]$, $[OH^-]$ will increase, and vice versa.
