Look up Cursors in the LabVIEW Help. You can create a cursor that "Snaps to" each of the points on your plot, and returns the X and Y values. With these data, you will be in a much better position to write a VI that lets you use a "Mouse-down" operation to modify the selected point in the graph. Note you may want to consider whether you want to move only vertically (X remains constant), only horizontally (Y constant), or freely (both X and Y change). You'll need to redraw the graph to show the change. Alternatively, you can put the cursor on the point you want to change, click where you want the point to go, interpret the Mouse Position when clicked as the new X, Y, then modify the Cursor's selected point's X and Y appropriately.
Bob Schor