Solve the given inequality graphically in a two-dimensional plane: $2x - 3y > 6$

(N/A) The graphical representation of $2x - 3y = 6$ is given as a dotted line in the figure below.
This line divides the $xy$-plane into two half-planes.
Select a point (not on the line),which lies in one of the half-planes,to determine whether the point satisfies the given inequality or not.
We select the point as $(0, 0)$.
It is observed that,
$2(0) - 3(0) > 6$ or $0 > 6$,which is false.
Therefore,the upper half-plane is not the solution region of the given inequality. Also,it is clear that any point on the line does not satisfy the given inequality because the inequality is strict $(>)$.
Thus,the solution region of the given inequality is the half-plane that does not contain the point $(0, 0)$,excluding the line itself.
The solution region is represented by the shaded region in the figure.