In this case c is a integer from -10..10:
ContourPlot[y == 3 x y - x y^2 + 1, {x, -5, 5}, {y, -4, 7}, FrameLabel -> Automatic](*If c=1 *)
ContourPlot[Evaluate@Table[y == 3 x y - x y^2 + c, {c, -10, 10}], {x, -5, 5}, {y, -4, 7}, FrameLabel -> Automatic]

Regards M.I.