For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]
For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]
Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]
