Let's begin by identifying key information given to us:
[tex]\begin{gathered} 2x-4y<8 \\ \text{Make ''y'' the subject of the equation, we have:} \\ \text{Add ''4y'' to both sides, we have:} \\ 2x-4y+4y<8+4y \\ 2x<8+4y \\ \text{Subtract ''8'' from both sides, we have:} \\ 2x-8<8-8+4y \\ 2x-8<4y\Rightarrow4y>2x-8 \\ 4y>2x-8 \\ \text{Divide through by ''4'', we have:} \\ \frac{4}{4}y>\frac{2}{4}x-\frac{8}{4} \\ y>\frac{1}{2}x-2 \end{gathered}[/tex]We will proceed to graph this inequality. We have:
[tex]\begin{gathered} y>\frac{1}{2}x-2 \\ x=-6 \\ y>\frac{1}{2}(-6)-2\Rightarrow y>-3-2\Rightarrow y>-5 \\ y>-5 \\ \\ x=0 \\ y>\frac{1}{2}(0)-2\Rightarrow y>0-2\Rightarrow y>-2 \\ y>-2 \\ \\ x=6 \\ y>\frac{1}{2}(6)-2\Rightarrow y>3-2\Rightarrow y>1 \\ y>1 \end{gathered}[/tex]The graph is attached below:
