How to know which side of a line will a halfspace $a^Tx \geq c$ fill?

Question

So given a half-space $a^Tx \geq c$, or $a^Tx \leq c$, how can you tell which "side" of the line $a^Tx = c$ will the space fill? By side I mean that region of space $\mathbb{R}^n$ that belongs to the half-space.And moreover why that "side" in particular. Sure in cases like $n = 2, 3$ one can perform computations, but having an idea how to visualize the half-space should help in convex optimization and linear algebra.