Converting the inequality into equation we get 3x + 4y = 12. This line meets x-axis at (4, 0) and y-axis at (0, 3). Joining these two points we obtain the straight line represented by 3x + 4y = 12. This straight line divides the plane in two parts. One part contains the origin the other does not contain the origin. Clearly, (0, 0) satisfies the inequality 3x + 4y ≤ 12. So, the region represented by 3x + 4y ≤ 12 is the region containing the origin as shown in Fig.
