How do you move the entire path at once?

From what I can see, you could either:

• Leave it where it is and adjust the Anchor for the layer.  This shifts the text relative to its position
  or
• Create a Null Object, parent the layer to that and move that.  All the position changes will still happen to the layer, but its position is now based on the null layer and not the comp.

You could also (I'd suggest reading this really quickly then ignoring it) precompose it or turn it into an essential graphic for reuse with different text or use expressions like Rick suggests or add a point control to the existing position using an expression like value+effect("Point Control")("Point") and then update the point control values... And I'm sure there's other options too.

You can attach the path to the text layer if the position of the text layer is animated. 

You can use sourceRectAtTime() to create an expression that always figures out where the bottom of the text layer is.

If you are using a text animator to move the text layer, you can tie those values to the position property of the line.

Uploaded screenshots that are cropped tell us nothing about your workflow. Select both layers, press the U key twice to show all of the modified properties of both layers, take a screenshot of the entire UI, then drag it to the reply field or copy and paste it to the reply field on the forum instead of uploading it with the "Drag & drop here..." button so we can see it without downloading and we can probably help you figure out a solution.

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