The given inequality is
$y+8 \geq 2x$
Consider the equation $y+8 =2x$
We see that $(4,0)$ and $(0,-8)$ Satisfy the given equation .
The graphical representation of the line $y+8=2x$ is given below
Step 2 :
The line divides the XY plane into two region I and II select a point not on the line say (0,0) in the half plane I , We see that
$0+8 \geq 2(0)$
$8 \geq 0$ is true.
$\therefore $ The half plane II is not a solution region of the given inequality .
The Solution region of the given inequality is the half plane I containing (0,0) including the points on the line .