Answer
The graph is shown below.
Work Step by Step
The given inequality is
$-x+4y\gt -12$
Graph $-x+4y=-12$. Use a dashed line because the inequality symbol is $ \gt$.
Test $(0,0)$.
$\Rightarrow -x+4y\gt -12$
$\Rightarrow -(0)+4(0)\gt -12$
$\Rightarrow 0+0\gt -12$
$\Rightarrow 0\gt -12$
Hence, $(0,0)$ is a solution, shade the half-plane that contains $(0,0)$.
