How to swap my iPhone iTunes thats on my laptop to my mac computer instead?

I've recently got a new mac, but I want to start downloading music onto my mac iTunes into my iPhone so I don't need to go on my laptop, I've tried but I don't know how? I want to connect my iPhone to my mac iTunes I stead of my other one but I want to keep all my old music still, need help

Copy the music from your iPhone to your laptop and email it to your mac. Download the music from the email you sent yourself and plug in the phone and sync it with your old music (from the email)
with the music on your mac.

How to Transfer an iTunes Playlist to a MacBook
Read more: http://www.ehow.com/...z2YTz8RHvq

How to Transfer Music From an iPhone to a Mac http://www.ehow.com/...e-mac.html

How to Transfer Music From an iPhone to a Mac
Read more: http://www.ehow.com/...z2YTzvd6CZ

iPhone Support, View topics, resources and contact options.http://www.apple.com/support/iphone/

This article is an overview of how to sync your iOS device with iTunes on your computer using USB or Wi-Fi.http://www.apple.com/support/iphone/syncing/