Cant Update Records Related ID in Pivot :(

So once again I'm having issues with some Many to Many functions. I have 2 models in a Many to Many relationship, Plays and Conferences. I'm simply trying to allow a user to link a play to another conference by replacing the related conference id (in pivot table) with the id value they choose in the select box. With Eloquent.

public function update(PlaysEditRequest $request, $id)
    {
        // get play matching uri id
        $play = Play::findOrFail($id);

        // get form data
        $form_data = $request->all();

        // if photo uploaded, create file name, move to images/plays dir, create record, assign record id to form data id
        if($file = $request->file('photo_id')){

            $file_name = time() . '-' . $file->getClientOriginalName();

            $file->move('images/plays', $file_name);

            $photo = Photo::create(['path'=> $file_name]);

            $form_data['photo_id'] = $photo->id;

        }



        // get selected conference
        $conference = Conference::findOrFail($form_data['conference_id'])->pluck('id')->first();

        $conference->save($form_data['conference_id']);

        // update record with form data
        $play->update($form_data);

        // go to conference related plays table & relate the new play to the conference id in the pivot table
        //$conference->pluck('id')->first()->save($form_data['conference_id']);

        $plays = Play::all();

        // create notification
        Session::flash('play_updated', 'Success! The play was successfully updated.');

        return view('admin.plays.index',compact('plays'));

    }

I'm getting different issues from "Call to a member function save() on integer" to some undefineds.. I believe in figuring it yourself as you learn more, but I'm under a deadline and need to move past this. Any ideas? Thanks!