I think this is what you want if you aren't used to editing. If it's complex then I misunderstood the problem. Turn on snapping for vertices to the point layer. Select line, choose modify feature for your task, hover the mouse over the vertice until it changes with a rectangular shape (not the crosshair which would move the whole selection), click and move the vertice to the point and it should snap in place. If you are using 10 the process may be slightly different depending on your snapping and feature template settings. On my test install of 10 I'm using the classic versions of both.