Answer
The graph is shown below.
Work Step by Step
The given inequality is
$5x+10y\lt 40$
Graph $5x+10y=40$. Use a dashed line because the inequality symbol is $ \lt$.
Test $(0,0)$.
$\Rightarrow 5x+10y\lt 40$
$\Rightarrow 5(0)+10(0)\lt 40$
$\Rightarrow 0+0\lt 40$
$\Rightarrow 0\lt 40$
True.
Hence, $(0,0)$ is a solution, shade the half-plane that contains $(0,0)$.
