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# Solve the given inequality graphically in two -dimensional plane. $-3x+2y \geq -6$

Toolbox:
• To represent the solution of linear inequality of one or two variable in a plane if the inequality involves $'\geq'$ or $' \leq$ we draw the graph of the line as a thick line to indicate the line is included in the solution set.
• If the inequality involves $'>'$ as $'<'$ we draw the graph of the line using is not included in the solution set.
• To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
• We consider the corresponding equation $ax+by =c$ which represents a straight line This line divides the plane into two half planes I and II
• We take any point in I half plane and check if it satisfies the given inequality will be one half plane (called solution region ) Containing the point satisfying the inequality
The given inequality is $-3x +2y \geq -6$
Consider the equation $-3x +2y =-6$
We see that $(2,0)$ and $(0,-3)$ satisfy the equation.
The graphical representation of the line is given below,
Step 2:
The line divides the xy plane into two half planes I and II
Consider a point (0,0) in the half plane I.
We see that , $-3 (0) +2(0) \geq -6$
$0 \geq -6$ is true.
Therefore the half plane II is not the solution region.
Step 3:
Thus the solution region of the given inequality is the half plane I containing the point (0,0) including the points on the line.
It is represented by the shaded region.