Question

On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.
Which linear inequality is represented by the graph

Answer 1

The line through (0, −1) and (3, 0) has slope (0 − (−1))/3 = 1/3, so its equation is y = (1/3)x − 1. The line is solid so the inequality is ≥ or ≤. Test a shaded point, e.g. (0,0): 0 ≥ (1/3)(0) − 1 = −1 is true, so the shaded half-plane is

y ≥ (1/3)x − 1

(Equivalently 3y ≥ x − 3 or x − 3y ≤ 3.)