Hi Davidb45,
There is a snap called "straight snap" that should be kicking in for this.. Do you possibly have straight snap unchecked under the snap options?? The other thing is you mention moving it on a "line"? Perhaps the line is not planar in X? Other ways would be to launch the Move command and drag out a construction line before you start to move the point.

If you need any help with what I just mentioned, just say and some more detail can be added.