Question

On a coordinate plane, two lines are shown. The first dashed line has a positive slope and goes through (negative 8, 0) and (0, 3). Everything below and to the right of the line is shaded. The second solid line has a negative slope and goes through (negative 5, 0) and (0, negative 2). Everything above and to the right of the line is shaded.
Which ordered pairs make both inequalities true? Check all that apply.

(−5, 5)
(0, 3)
(0, −2)
(1, 1)
(3, −4)

Answer 1

First line (dashed) through (-8,0) and (0,3): y < (3/8)x + 3.
Second line (solid) through (-5,0) and (0,-2): y ≥ (-2/5)x − 2.

Check each:

- (−5,5): y = 5, (3/8)(−5)+3 = 9/8 ≈ 1.125 → 5 < 1.125 false → no.
- (0,3): y = 3, (3/8)(0)+3 = 3 → 3 < 3 false (dashed line not included) → no.
- (0,−2): y = −2, (3/8)(0)+3 = 3 → −2 < 3 true; (−2/5)(0)−2 = −2 → −2 ≥ −2 true → yes.
- (1,1): y = 1, (3/8)(1)+3 = 3.375 → 1 < 3.375 true; (−2/5)(1)−2 = −2.4 → 1 ≥ −2.4 true → yes.
- (3,−4): y = −4, (−2/5)(3)−2 = −3.2 → −4 ≥ −3.2 false → no.

Therefore the ordered pairs that make both inequalities true are (0, −2) and (1, 1).