Given x + y ≥ 4

⇒ y ≥ 4 - x

Consider the equation y = 4 - x.

Finding points on the coordinate axes:

If x = 0, the y value is 4 i.e, y = 4

⇒ the point on the Y axis is A(0,4)

If y = 0, 0 = 4 - x

⇒x = 4

The point on the X axis is B(4,0)

Plotting the points on the graph: fig. 1a

Now consider the inequality y ≥ 4 - x

Here we need the y value greater than or equal to 4 - x

⇒ the required region is above point A.

Therefore the graph of the inequation x + y ≥ 4 is fig. 1b

Fig 1a

Fig 1b