Draw the graph `x-y ge 0` in the Cartesian plane.

Explanation

(a) We first draw the line `x -y =0`, i.e., `x =y`,
`{:(x,,-2,,0,,2),(y,,-2,,0,,2):}`
Plot the ordered pars `(-2, -2), (0, 0), (2, 2)` and then join them with a line.
(b) For shading the required region, we consider any point in one of the half planes. Let us consider the point `(1, -2)` and substitute the coordinates of the point in the inequation
`x-y ge 0 rArr 1- (-2) ge 0`

`rArr 3 ge 0` which is true
`therefore (1, -2)` belongs to the graph of the inequality `x-y ge0`.
Now, shade the region (half plane) which includes the point `(1, -2)`.
For shading the regions of linear inequations which are not passing through origin. Substitute the origin (0, 0) in the given inequation. If the inequality arrived is true, then the origin belongs to the region represented by the graph and shade the origin side of half plane. If the inequality arrived is false, then the origin does not belong to the origin represented by the graph and shade the half plane that does not contain the origin.