If a, b, c > 0 and ax+bygt c , then its graph represents:

The correct answer is Option (2) → the half plane that neither contains the origin nor the points on the line \( ax+by=c \).

At the origin the left side of the inequality is

    \( \displaystyle a(0)+b(0)=0 \)

Since c > 0, \( 0\gt c \) is false, so the origin does not lie in the region. The inequality is strict, so the points of the line \( ax+by=c \) are also excluded.

Hence the graph is the half plane that contains neither the origin nor any point of the line.