Question

Solve the following inequation graphically in the two-dimensional plane.
4x + 5y ≤  40

Answer 1

Consider the equation 4x + 5y ≤ 40
Two points required to draw the line are given by the table

x	10	0
y	0	8

The two points on the coordinate axes are (10, 0) and (0, 8) respectively.
Since the inequality is 4x + 5y ≤  40,  the origin O (0, 0) will satisfy the inequation as 4x + 5y ≤  40
i.e. 0 ≤ 40. 
The solution set is in the part of the plane towards the origin.