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?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1

Answer 1

The line through (0, −1) and (3, 0) has slope (0 − (−1))/(3 − 0) = 1/3, so its equation is y = (1/3)x − 1. The line is solid (inclusive) and the shaded region is above it, so the inequality is

y ≥ (1/3)x − 1.