Hello everybody!

I am trying to create a graph displaying the substitution effects of a change (decrease) in the price of good Y and I am trying to combine the legends for each function. I am somewhat new to Mathematica and have reached a roadblock. It seems like I need to use PlotLegends but I don't understand what I need to do. Here are two versions of my attempts:

f[x_] := 4/x
g[x_] := 9/x
a[x_] := -1 x + 6
b[x_] := -2.25 x + 6
h[x_] := -1 x + 4

pos = {Right, Top};
Show[{Plot[f[x], {x, -6, 15}, PlotStyle -> Blue], 
  Plot[g[x], {x, 0, 15}, PlotStyle -> Green], 
  Plot[a[x], {x, 0, 6}, PlotStyle -> Red], 
  Plot[b[x], {x, 0, 2.667}, PlotStyle -> Red], 
  Plot[h[x], {x, 0, 4.1}, PlotStyle -> Yellow]}, 
 ListPlot[{f[x], g[x], a[x], b[x], h[x]} -> {"\[ScriptCapitalU]", 
    "\[ScriptCapitalU]'", "After Price\[DifferenceDelta]", 
    "Before Price\[DifferenceDelta]", "Hypothetical Budget Line"}, 
  ListPlot[{{1.333, 3}, {2, 2}, {3, 3}} -> {"A", "B", "C"}] , 
  GridLines -> Automatic, PlotRange -> {{0, 10}, {0, 6.5}}, 
  AxesOrigin -> {0, 0}, 
  AxesLabel -> {HoldForm[Good x], HoldForm[Good y]}, 
  PlotLabel -> HoldForm[Price of good y is cheaper], 
  LabelStyle -> {GrayLevel[0], Bold, Italic}]]

Second attempt:

f[x_] := 4/x
g[x_] := 9/x
a[x_] := -1 x + 6
b[x_] := -2.25 x + 6
h[x_] := -1 x + 4

pos = {Right, Top};
Show[{Plot[f[x], {x, -6, 15}, PlotStyle -> Blue, 
   PlotLegends -> "\[ScriptCapitalU]"], 
  Plot[g[x], {x, 0, 15}, PlotStyle -> Green, 
   PlotLegends -> "\[ScriptCapitalU]'"], 
  Plot[a[x], {x, 0, 6}, PlotStyle -> Red, 
   PlotLegends -> "After Price\[DifferenceDelta]"], 
  Plot[b[x], {x, 0, 2.667}, PlotStyle -> Red, 
   PlotLegends -> "Before Price\[DifferenceDelta]"], 
  Plot[h[x], {x, 0, 4.1}, PlotStyle -> Yellow, 
   PlotLegends -> "Hypothetical Budget Line"]}, 
 ListPlot[{{1.333, 3}, {2, 2}, {3, 3}} -> {"A", "B", "C"}] , 
 GridLines -> Automatic, PlotRange -> {{0, 10}, {0, 6.5}}, 
 AxesOrigin -> {0, 0}, 
 AxesLabel -> {HoldForm[Good x], HoldForm[Good y]}, 
 PlotLabel -> HoldForm[Price of good y is cheaper], 
 LabelStyle -> {GrayLevel[0], Bold, Italic}]

Thank you so much for your help!