x[t_, s_] = t + s
y[t_, s_] = t + s
u[t_, s_] = t + s
t = 0
p1 = {RGBColor[0, 1, 0], Thickness[0.01]}
g1 = 
      ParametricPlot3D[{x[t, s], y[t, s], u[t, s], p1}, {s, -1, 
          1}]

⁃  Graphics3D  ⁃
u[x_, 
        y_] = (1/2) x + (1/2) y
g2 = 
      Plot3D[u[x, y], {x, -1, 1}, {y, -1, 1}]

Show[g1, g2]