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

We draw the graph of the equation y = -2.

Clearly it is a line parallel to x-axis at a distance of 2 units below it. The line y - -2 divides the xy-plane into two regions one below it and the other above it.

Consider the point 0(0, 0). We find that (0, 0) does not satisfy the inequality y < - 2 because 0 < -2 which is not true.

So, the region represented by the given inequality is the region not containing the origin as shown in the Fig. 6.24, by the shaded region excluding all points on the line.