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
y > 3x − 1

Answer 1

Line through (0,-1) and (3,0) has slope (0−(−1))/(3−0)=1/3, so equation y = (1/3)x − 1. The line is solid (inclusive). A point in the shaded region (for example (0,0)) gives 0 ≥ (1/3)(0) − 1 → 0 ≥ −1, true. So the inequality is

y ≥ (1/3)x − 1.