Q.Represent the solution set of $x-2y>4$ graphically.

Draw the boundary dashed (strict $>$), then test the origin.

Step 1 — Boundary line. The equation $x-2y=4$ has intercepts $(4,0)$ (put $y=0$) and $(0,-2)$ (put $x=0\Rightarrow-2y=4\Rightarrow y=-2$). Join them.

Step 2 — Solid or dashed. The sign is strict $>$, so the line is dashed and is not part of the solution.

Step 3 — Test point. Origin $(0,0)$ (the line does not pass through it):

Step 4 — Shade. Because the origin does not satisfy the inequation, shade the half-plane on the opposite side from the origin. That open region (line excluded) is the solution. …

Mis-locating the $y$-intercept as $(0,2)$ instead of $(0,-2)$; and drawing a solid line …