Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
Which point is a solution to the linear inequality y < Negative one-halfx + 2?

(2, 3)
(2, 1)
(3, –2)

Answer 1

Check each point in y < (-1/2)x + 2.

For (2,3): 3 < (-1/2)(2)+2 = 1 → false.
For (2,1): 1 < 1 → false (strict inequality).
For (3,−2): −2 < (-1/2)(3)+2 = 0.5 → true.

So (3, −2) is a solution.