Question

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded.
Which points are solutions to the linear inequality y < 0.5x + 2? Select three options.


(–3, –2)
(–2, 1)
(–1, –2)
(–1, 2)
(1, –2)

Answer 1

Substitute each point into y < 0.5x + 2:

- (–3, –2): RHS = 0.5(–3)+2 = 0.5, and –2 < 0.5 → true.
- (–2, 1): RHS = 0.5(–2)+2 = 1, and 1 < 1 → false (point is on the line).
- (–1, –2): RHS = 0.5(–1)+2 = 1.5, and –2 < 1.5 → true.
- (–1, 2): RHS = 1.5, and 2 < 1.5 → false.
- (1, –2): RHS = 0.5(1)+2 = 2.5, and –2 < 2.5 → true.

Answers: (–3, –2), (–1, –2), (1, –2).