We draw the graph of the equation 3x + 4y = 12. The line passes through the points (4, 0), (0, 3). This line is represented by AB.
Now consider the inequality 3x + 4y ≤ 12
Putting x = 0, y = 0
0 + 0 = 0 ≤ 12, which is true.
∴ Origin lies in the region of 3x + 4y ≤ 12
The shaded region represents the inequality 3x + 4y ≤ 12