JAMB 1998 · UME · Q18

The shaded area in the graph represents

Worked solution (try it first)

The line through $(0, 3)$ and $(2, 0)$ has gradient $\frac{0 - 3}{2 - 0} = -\frac32$ and $y$ -intercept 3, so $y = -\frac32x + 3$ .
Multiply by 2 and rearrange: $3x + 2y = 6$ .
Test the origin: $0 \ge 6$ is false, and the origin is not shaded, so the region is $3x + 2y \ge 6$ .
The shading is in the first quadrant, so $x \ge 0$ and $y \ge 0$ too: option D.