Solve 2 y - 3 ≥ 0 graphically in a two dimensional plane.

Given 2 y - 3 ≥ 0 Consider the equation 2 y - 3 = 0 ⇒ 2 y = 3 ⇒ y = 1 . 5 But, y = 1 . 5 represents a line parallel to x -axis at a distance of 1 . 5 units from it. We draw the line y = 1 . 5 , making it thick. If we put y = 0 in the given inequation, we get - 3 ≥ 0 , which is false. So, y = 0 does not satisfy the given inequation. So, we shade the region above the line y = 3 2 , as shown below

Solve 5 y - 4 ≤ 0 graphically in a two dimensional plane.

Given 5 y - 4 ≤ 0 Consider the equation 5 y - 4 = 0 ⇒ 5 y = 4 ⇒ y = 4 5 = 0 . 8 But, y = 0 . 8 represents a line parallel to x -axis at a distance of 0 . 8 units from it. We draw the line y = 0 . 8 , making it thick. If we put y = 0 in the given inequation, we get - 4 ≤ 0 , which is true. So, y = 0 satisfy the given inequation. Solution region consists of the line y = 0 . 8 and we shade the region below the line y = 0 . 8 , as shown below