DynamicModule[{k}, Panel[
Column[{
Row[{"a", " ", Slider[Dynamic[k], {1, 9, 0.3}]}],
With[{a = k},
Dynamic@ContourPlot[t + Sin[w t] == a, {t, 0, 10}, {w, -5, 5},
PlotPoints -> 25, ImageSize -> 300,
PlotLabel -> "w vs.t given a", FrameLabel -> {"t", "w"}
]]}]
]
]