Question

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (2, 0). Everything to the right of the line is shaded.
The solutions to the inequality y ≤ 2x − 4 are shaded on the graph. Which point is a solution?

(−1, 1)
(1, −1)
(3, 2)
(2, 3)

Answer 1

First write the line: y = 2x − 4. Test each point in y ≤ 2x − 4:

- (−1, 1): 1 ≤ 2(−1) − 4 = −6 → false
- (1, −1): −1 ≤ 2(1) − 4 = −2 → false
- (3, 2): 2 ≤ 2(3) − 4 = 2 → true
- (2, 3): 3 ≤ 2(2) − 4 = 0 → false

So (3, 2) is a solution.