$\begin{align}  & \text{The given coordinate are }({{x}_{1}},{{y}_{1}})=(-4,0) \\ & \text{          }({{x}_{2}},{{y}_{2}})=(0,2) \\ & \text{Using the two point form equation } \\ & \frac{y-{{y}_{1}}}{x-{{x}_{1}}}=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & \frac{y-0}{x-(-4)}=\frac{2-0}{0-(-4)} \\ & \frac{y}{x+4}=\frac{2}{4} \\ & \frac{y}{x+4}=\frac{1}{2} \\ & 2y=x+4 \\ & -x+2y=4 \\ & \text{Introducing the inquality sign} \\ & -x+2y\le 4 \\ & \text{Comparing the two equation  } \\ & -x+2y\le 4\text{  and }px+qy\le 4 \\ & \text{shows that }p=-1,\text{ }q=2 \\ & (p,q)=(-1,2) \\\end{align}$