Solve the given inequality graphically in a two-dimensional plane: $2x + y \geq 6$

(N/A) The graphical representation of the line $2x + y = 6$ is shown in the figure.
This line divides the $xy$-plane into two half-planes,$I$ and $II$.
Select a point (not on the line),which lies in one of the half-planes,to determine whether the point satisfies the given inequality.
We select the point $(0, 0)$.
It is observed that,
$2(0) + 0 \geq 6$ or $0 \geq 6$,which is false.
Therefore,half-plane $I$ is not the solution region of the given inequality. Also,it is evident that any point on the line satisfies the given inequality.
Thus,the solution region of the given inequality is the shaded half-plane $II$ including the points on the line.