Question

On a coordinate plane, 2 lines are shown. The first solid straight line has an equation of y greater-than-or-equal-to negative one-fifth x + 1, has a negative slope, and goes through (negative 5, 2) and (0, 1). Everything above the line is shaded. The second dashed solid line has equation y less-than 2 x + 1, has a positive slope, and goes through (negative 2, negative 3) and (0, 1). Everything to the right of the line is shaded.
Which ordered pairs make both inequalities true? Check all that apply.

(–2, 2)
(0, 0)
(1,1)
(1, 3)
(2, 2)

Answer 1

We need points that satisfy both
y ≥ −(1/5)x + 1 and y < 2x + 1.

Check each:

- (−2, 2): First: 2 ≥ 1.4 (true). Second: 2 < −3 (false). → no
- (0, 0): First: 0 ≥ 1 (false). → no
- (1, 1): First: 1 ≥ 0.8 (true). Second: 1 < 3 (true). → yes
- (1, 3): First: 3 ≥ 0.8 (true). Second: 3 < 3 (false, equality not allowed). → no
- (2, 2): First: 2 ≥ 0.6 (true). Second: 2 < 5 (true). → yes

Answers: (1, 1) and (2, 2).