Define the MouseMove event for line

There is no such thing. The line is not an object of a type implementing events. Moreover, the line is not an object at all.

All you can do is adding an event handler to the control used to draw your line on. Alternatively, you can override mouse-handling virtual methods. How this event is related to the line — is all your business. You can define some criteria used to find out of a mouse is "close" to some point of a line at the moment of pressing a mouse key down. The schema is this:

class MyContol : System.Windows.Forms.Control {

    public MyContol() {
        ThePen = new System.Drawing.Pen(/*...*/); // to be disposed
        //important to avoid flicker:
        SetStyle(System.Windows.Forms.ControlStyles.OptimizedDoubleBuffer);
        SetStyle(System.Windows.Forms.ControlStyles.AllPaintingInWmPaint)
        //...
    }

    protected override void Dispose(bool disposing) {
        if (disposing)
            ThePen.Dispose(); //imporant!
    }

    protected override void OnPaint(PaintEventArgs e) {
        //...
        System.Drawing Point p1 = // get from your data model
        System.Drawing Point p2 = // get from your data model
        e.Graphics.DrawLine(ThePen, p1, p2);
        //...
    }

    protected override void OnMouseDown(MouseEventArgs e) {
        base.OnMouseDown(e);
        //check up with your data model
        //...
    }
    protected override void OnMouseUp(MouseEventArgs e) {
        base.OnMouseUp(e);
        //check up with your data model
        //...
    }
    protected override void OnMouseMove(MouseEventArgs e) {
        base.OnMouseMove(e);
        //check up with your data model
        //...
        //...
        if (/*...*/)
           Invalidate(); //important, otherwise WM_PAINT is not sent, OnPaint not called
    }

    System.Drawing.Pen ThePen;
}

The key is your data model here: you need to represent all you draw in some pure-data model and keep in the memory of you class. Update of the model by mouse, keyboard, controls, etc. needs Invalidate to be called. You can use Invalidate with a parameter (Rectangle or Region) to redraw only a part of the scene.

A bonus advice: implement your rendering method as a separate method of the same class, make a parameter of the type Graphics. In this way, you can call it no only from OnPaint, but from somewhere else using different instance of the Graphics: of a bitmap for exporting the graphics to a bitmap, of a printer document to print it, etc.

—SA