Graph of an inequality
We know that the boundary line is given by the following equation:
4x + 3y = -3
Then, there are only two possible inequalities:
1. 4x + 3y ≥ -3
2. 4x + 3y ≤ -3
In order to find out which of the two cases is this, we are going to select any point of the shaded region. This time we are going to select
the point (-5, -5)
where
x = -5 and y = -5.
We replace those x and y values and see which of both is true:
4x + 3y
↓ replacing with (-5, -5) = (x, y)
4(-5) + 3(-5)
= -20 - 15
-35
The first case says that
1. 4x + 3y ≥ -3
this is not true because
-35 ≥ -3 is not true
The second case says that
2. 4x + 3y ≤ -3
which is true because
-35 ≤ -3 is correct
Answer: the inequality that represents the shaded region is 4x + 3y ≤ -3
