Draw the region 2x - 3y ≥ 6. Find the intercepts of its boundary line…

Step 1. The intercepts. Put $y = 0$: $2x = 6$, so $x = 3$. Put $x = 0$: $-3y = 6$, so $y = -2$. The line joins $(3, 0)$ and $(0, -2)$.

Step 2. The test. At the origin $2(0) - 3(0) = 0$, and $0 \ge 6$ is false. So shade the side that does not hold the origin.

Step 3. The line. The sign is $\ge$, which includes equality, so the line is solid.

Step 4. The point. $2(5) - 3(1) = 7$, and $7 \ge 6$ is true. So $(5, 1)$ is in the region, on the shaded side.