You can verify if a point is a solution to the linear inequality by replacing the value of x in the right member of the inequality and checking wheter the y-value meets the condition.
For example, if you want to check if the point (2, 5) is a solution of the inequality, follow these steps:
1) Replace 1 for x, in the second member of the inequality: -1/2 * (1) + 2 = -1/2 + 2 = (-4 + 2) / 2 = -2/2 = - 1,
2) Compare the value of y-coordinate of the point with the value obtained from above: 5 is not < -1.
3) Conclusion: point (2,5) is not a solution to the linear inequality y < -1/2x + 2.
Other example:
Point (2, 0)
1) Replace x: -1/2(2) + 2 = -1 + 2 = 1
2) Compare: 0 < 1
3) Conclusion: the point (2,0) is a solution to the linear inequality.
