f[x_, y_] = x^3 + x^2*y^3 - 2*y^2

p1 = Plot3D[f[x,y], {x,-2,2}, {y,-2,2}]

fx[y_] = {1,y,f[1,y]}

fy[x_] = {x,1,f[x,1]}

p2 = ParametricPlot3D[fx[y], {y,-2,2},PlotRange->{{-2,2},{-10,10}},PlotStyle->{Blue, Thick}];

p3 = ParametricPlot3D[fy[x], {x,-2,2}, PlotRange->{{-2,2},{-10,10}},PlotStyle->{Green, Thick}];

Show[p1,p2,p3,PlotRange->{{-2,2},{-2,2},{-10,10}}]

Lx[x_] = {1+x,1,5*x}
p4 = ParametricPlot3D[Lx[x], {x,-2,2},PlotRange->{{-2,2},{-10,10}},PlotStyle->{Cyan, Thick}];

Ly[y_] = {1,1+y,-y}
p5 = ParametricPlot3D[Ly[y], {y,-2,2},PlotRange->{{-2,2},{-10,10}},PlotStyle->{Yellow, Thick}];

Show[p1,p2,p3,p4,p5,PlotRange->{{-2,2},{-2,2},{-10,10}}]

p6 = Plot3D[5*(x-1)-(y-1),{x,-2,2},{y,-2,2},PlotStyle->{LightGreen}]

Show[p1,p2,p3,p4,p5,p6,PlotRange->{{-2,2},{-2,2},{-10,10}}]

Show[p1,p6]