For a line ax + by + c = 0, substitute two points P1 and P2. If the expressions ax1 + by1 + c and ax2 + by2 + c have the same sign, P1 and P2 are on the same side of the line. If they have opposite signs, they are on opposite sides. The origin is on the side where the sign of c determines: if c > 0, origin gives positive value (since a0 + b0 + c = c). This is useful for solving inequalities and region-based problems.