Show[RegionPlot[x+2*y ≥   2&&2*x+y ≥ 3&&x≥  0&& y≥ 0,{x,-2,5},{y,-2,5},PlotLegends  ->"Expressions",Axes->True,AxesStyle->Arrowheads[0.05]],Plot[-(1/8)x +(1/4),{x,-2,5},PlotLegends -> "Expressions",PlotStyle -> {Red,DotDashed}],Plot[((-3)/2)x +(7/3),{x,-2,5},PlotLegends -> "Expressions",PlotStyle -> {Green,Dashed}],
Plot[-8*x +3,{x,-2,5},PlotLegends -> "Expressions",PlotStyle -> {Yellow,Yellow}]]

(Legended[, ({{(LineLegend[-((3 x)/2)+(7/3)])}, {(LineLegend[-(x/8)+(1/4)])}, {(SwatchLegend[x+2 y≥2∧2 x+y≥3∧x≥0∧y≥0])}, {(LineLegend[-8 x+3])}})])