Final answer:
Points A (0,0), B (1,2), and C (2,1) are solutions to the linear inequality y < 0.5x + 2 because, for each point, the y-value is less than half of the x-value plus 2.
Step-by-step explanation:
To determine which points are solutions to the linear inequality y < 0.5x + 2, we must check if the y-value of each point is less than half of the x-value plus 2.
- For point A (0,0), substituting x = 0 into the inequality, we get 0 < 0 + 2, which is true. So, point A is a solution.
- For point B (1,2), substituting x = 1 into the inequality, we get 2 < 0.5 × 1 + 2, which simplifies to 2 < 2.5, which is also true. So, point B is a solution.
- For point C (2,1), substituting x = 2 into the inequality, we get 1 < 0.5 × 2 + 2, which simplifies to 1 < 3, which is true. Thus, point C is a solution.
- For point D (3,5), substituting x = 3 into the inequality, we get 5 < 0.5 × 3 + 2, which simplifies to 5 < 3.5, which is false. Therefore, point D is not a solution.
Hence, the points that are solutions to the linear inequality y < 0.5x + 2 are A (0,0), B (1,2), and C (2,1).