What Is A "Line Rate" Switch?

I said in a post recently that I would describe what "line rate" meant in a switch.  First, I'm going to give an elementary description, and then I can move on to a real live example.
First, lets say we have a 12 port switch.  That is all it has on the front, is just 12 1Gig ports, and nothing else.
Really, this means that if you give the switch everything the network has got, on its connected ports, can it pass all that traffic?  So here is how we calculate our first example.   We have 12 1Gig ports.  We take 12, and multiply it by 2 (TX and RX) to get 24Gbps.  Our switch backplane (on the inside of the switch) has to be rated at 24Gpbs for this to be line rate.
Think of it like this.  If I have 12 water pipes going into the drain, and I fill all 12 of them up.  Can the end pipe where it all dumps into handle it?  Same principle.  Can the switch handle all the traffic coming in if it was completely maxed out on its ports?

Above is kindof a visual.  If water is coming in from the left side, and it goes to the right, will that second pipe handle it?  In this case, yes is the answer.
Now, here is a real life example.  How about the Brocade 6610?  There is 48 1Gig ports (TX and RX) that equals 96Gig (48 X 2).  Then you have 8 10Gig ports.  Thats another 80Gig X 2 = 160Gig.  Then, there is another 4 40Gig ports on the back, which totals 4 X 40 = 160 X 2 (TX and RX) = 320Gig.  Now, add 320Gig + 160Gig + 96Gig.  That better give us 576Gig!  And, it does.  So the Brocade ICX6610 is considered, and rightly so, a "line rate" switch.
Now lets consider the Cisco 3850-48P.  You have 48 1Gig ports (96Gig with TX and RX), 4 10Gig ports (80Gig total with TX and RX), and up to 2 40Gig ports in an add on module (160Gig total).  Thats 96 + 80 + 160 = 336Gig.  Uh oh, the switching backplane only rates at 176Gbps.  Thats a problem.  If you subtract the 2 40Gig ports that come on that add on module, then you get 96 + 80 = 176Gig, which is "line rate".  Be aware if you add that 2 port 40Gig module.