Answer:
To determine if a given point is a solution to the inequality y > -x - 3, we need to substitute the values of the point into the inequality and check if the resulting inequality is true.
Let's start with the point (0, 0).
Substituting the values x = 0 and y = 0 into the inequality, we get:
0 > -0 - 3
Simplifying the right side of the inequality, we have:
0 > -3
Since the inequality 0 > -3 is true, we can conclude that (0, 0) is a solution to the inequality y > -x - 3.
Now, let's check the point (-2, -2).
Substituting the values x = -2 and y = -2 into the inequality, we get:
-2 > -(-2) - 3
Simplifying the right side of the inequality, we have:
-2 > 2 - 3
-2 > -1
Since the inequality -2 > -1 is false, we can conclude that (-2, -2) is not a solution to the inequality y > -x - 3.
From the graph of the inequality, we can also determine if a point is a solution. The inequality y > -x - 3 represents a half-plane above the line y = -x - 3.
If we graph this line and shade the region above it, any point located in the shaded region will be a solution to the inequality. Conversely, any point located below the line will not be a solution.
Therefore, we can visually determine that (0, 0) is a solution as it lies in the shaded region above the line. On the other hand, (-2, -2) is not a solution as it lies below the line.
In summary:
- (0, 0) is a solution to the inequality y > -x - 3.
- (-2, -2) is not a solution to the inequality y > -x - 3.
Explanation: