The graph of the inequality 3x - 2y gt 6 is

The correct answer is Option (2) → Half plane that neither contains origin nor the points on the line \(3x - 2y = 6\)

The line \(3x - 2y = 6\) divides the plane into two half planes, and a linear inequality holds on exactly one of them.

Test the origin (0, 0):

    \(3(0) - 2(0) = 0\), and \(0 \gt 6\) is false

So the region is the half plane on the side away from the origin. The inequality is strict (\(\gt\), not \(\ge\)), so the points on the line \(3x - 2y = 6\) itself are not included.