The procedure for drawing the graph of inequality is similar to that of a linear graph.
The additional point to note here will be the shading of regions in the graph of inequality.
Boundaries within regions
The required boundary of a particular region is described by the equality sign =
However if the inequality sign is:
1. \( \scriptsize < \: or \: > \): the points on the boundary region are to be excluded, and for this, broken lines are used to draw the graph.
2. \( \scriptsize \leq \: or \: \geq \) : the points on the boundary region are included, and for this, continuous (straight unbroken) lines are used.
1. Draw the graph of 3x + 2y < 12
When x = 0, y = 6 When y = 0, x = 4
2. Draw the graph of 4x + 3y ≥ 24
When x = 0, y = 8
When y = 0, x = 6
Simultaneous linear inequalities in two variables
Show on a graph the region which contains the solution of the simultaneous inequalities
4x – y ≤ 8
3x +2y > 12
Let us consider the inequality 4x – y ≤ 8 first.
To get the boundary line, first make y the subject
i.e 4x – y = 8
-y = 8 – 4x
y = -8 + 4x
When x = 0, y = -8. This gives point (0, – 8)
When y = 0, x = 2. This gives points (2, 0)
Mark out these two points on your axis and then join them together with a solid line
We consider the second inequality 3x + 2y > 12.
To get the boundary line which must be a broken line.
When x = 0, y = 6. This gives point (0, 6)
When y = 0, x = 4. This gives points (4, 0).
The solution lies within the region bounded by area ABC.