JFT,
Motion paths are used to move an object (text, picture etc...) from point A
to point B. The dotted line is there to show you where the object is going
during the slideshow, in edit mode you will see it not in show mode however.
If you want to have a line appear while the object animates with a motion
path, you will have to draw it yourself and apply an entrance effect like
wipe. Make that animation start with previous so both will appear at the
same time.
You can draw the line on top of the motion path if you want, you can use the
green starting point and the red endpoint as the beginning and endpoint of
your line.
If you just want to animate a line appearing say from left to right no need
to apply a motion path, just apply an entrance effect in the custom
animation task pane. Apply the wipe from left effect and you are set.