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)
(–1, 3)

Answer 1

Plug each point into y < -1/2 x + 2.

(2,3): 3 < 1? No.
(2,1): 1 < 1? No (not strict).
(3,−2): −2 < 0.5? Yes.
(−1,3): 3 < 2.5? No.

So (3, −2) is a solution.