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Solve the following inequality graphically in two-dimensional plane: y< - 2

Solve the following inequality graphically in two-dimensional plane:

    Q9.    y < -2

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y < -2

Graphical representation of  y=-2  is given in graph below.

The line y < -2  divides plot in two half planes.

Select a point (not on the line y < -2) which lie in one of the half plane , to detemine whether the point satisfies the inequality.

Let there be a  point (1,2)

We observe 

                    i.e. 2< -2  , which is false.

Therefore, the half plane I  is not a solution region of given inequality i.e. y < -2.

Also, the point on the line does not satisfy the inequality.

Thus, the solution to this inequality is half plane II  excluding points on this line, represented by green colour.

This can be represented as follows: 

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