Solve the given inequality graphically in two-dimensional plane: y < - 2

Solution:

The graphical representation of y = - 2 is given as a dotted line in the figure below.

This line divides the XY plane into two half-planes.

Select a point (not on the line), which lies in one of the half-planes, to determine whether the point satisfies the given inequality or not.

We select the point as (0, 0). It is observed that, 0 < - 2, which is false.

Also, it is evident that any point on the line does not satisfy the given inequality.

Hence, every point below the line, y = - 2 (excluding all the points on the line), determines the solution of the given inequality

The solution region is represented by the shaded region as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.2 Question 9

Solve the given inequality graphically in two-dimensional plane: y < - 2

Summary:

A linear inequation y < - 2 is given. We have found that every point below the line, y = - 2 (excluding all the points on the line), determines the solution of the given inequality