The given inequality is $y <-2$
Consider the equation $y=-2$
The graph of the dotted line $y=-2$ is given below.
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Step 2:
The line $y=-2$ divides the XY- Plane into two half planes I and II
We select a point not on the line (0,0) in the half plane I.
We see that $0 < -2$ is false
Step 3:
Thus the half plane I containing the point (0,0) is not the solution region.
The solution region of the given inequality is the half plane II not containing the line .
It is represented by the shaded region.