Question

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 1) and (1, 0). Everything to the left of the line is shaded.
The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?

(2, 3)
(3, –2)
(2, 1)
(–1, 3)

Answer 1

Test each point in y ≤ −x + 1:

- (2, 3): 3 ≤ −2 + 1 = −1 → false
- (3, −2): −2 ≤ −3 + 1 = −2 → true
- (2, 1): 1 ≤ −2 + 1 = −1 → false
- (−1, 3): 3 ≤ 1 + 1 = 2 → false

So (3, −2) is a solution.