Answer :
Answer:
(-3, -2)
(-1, -2)
(1, -2)
Step-by-step explanation:
To determine which points are solutions to the linear inequality y < 0.5x + 2, we need to check each point by substituting the x and y coordinates into the inequality.
Given points:
- (-3, -2)
- (-2, 1)
- (-1, -2)
- (-1, 2)
- (1, -2)
Let's test each point:
For point (-3, -2):
[tex]y < 0.5x + 2 \\\\-2 < 0.5(-3) + 2 \\\\-2 < -1.5 + 2 \\\\-2 < 0.5 \quad \text{(True)}[/tex]
For point (-2, 1):
[tex]y < 0.5x + 2 \\\\1 < 0.5(-2) + 2 \\\\1 < -1 + 2 \\\\1 < 1 \quad \text{(False)}[/tex]
For point (-1, -2):
[tex]y < 0.5x + 2 \\\\-2 < 0.5(-1) + 2 \\\\-2 < -0.5 + 2 \\\\-2 < 1.5 \quad \text{(True)}[/tex]
For point (-1, 2):
[tex]y < 0.5x + 2 \\\\2 < 0.5(-1) + 2 \\\\2 < -0.5 + 2 \\\\2 < 1.5 \quad \text{(False)}[/tex]
For point (1, -2):
[tex]y < 0.5x + 2 \\\\-2 < 0.5(1) + 2 \\\\-2 < 0.5 + 2 \\\\-2 < 2.5 \quad \text{(True)}[/tex]
Therefore, the points that are solutions to the inequality y < 0.5x + 2 are:
- (-3, -2)
- (-1, -2)
- (1, -2)
When determining solutions using the graph of the given inequality:
- Points inside the shaded region satisfy the inequality and are solutions.
- Points on the boundary line do not satisfy the inequality and are not solutions because the inequality is strict (< or >).
- Points outside the shaded region do not satisfy the inequality and are not solutions.
