Concrete patio against the house
Typically when I pour concrete against a house foundation, (never pour concrete against any siding IMHO, it invites trouble later) I have an expansion joint set to the house. It can be cork, 1/2" thick by 4" tall set to the wall with short pins to hold it while pouring. There is a tar or asphalt impregnated expansion joint material too that may hold a straight line better with fewer fasteners.

The 1/8"/ft is a good number as mentioned by Jimmy fix-it. To set the slope, a form is set in place that sets the size (area) and the top level of the concrete surface. The form is also set at the recommended slope. 2X4s are usually used for this, then they are removed after a day or so. You will also need a concrete edger to ease the corner where the 2X forms are.

Usually pro concrete workers would not set anything within the 10 width, they don't need it, but you can set something at the middle if you choose, since an 8' screed board is a killer to pull if you don't have good help. It can either be a short piece of rebar driven in so the top is at the level for the concrete, strike your concrete in that area to the level dictated by the rebar, after the surface is set, drive the rebar further into the concrete so it is well below the surface. It works but it is easy to loose track of this pin while everything else is going on.

The other way to do the same is set a wood stake in the place you wish to use to set the top of the concrete, making sure the stake is tall enough to be well above the concrete finished surface, say anywhere between 6" to 1' above, (it can be more, but shorter would make the removal harder), set a screw or nail at the level of the concrete and when the level of concrete is set to the nail or screw, pull the stake out and plop a small amount of concrete while you are pouring to fill the void left by the removed stake. Yes you will need boots, and get in the middle of it.

When placing the concrete the edges are floated very close to the finished level, all around the edges. The pour will start from the farthest side, and the pour will proceed closer to the truck. Set the level at the house using a hand float to set the level to the expansion joint and work the far side and start going down the long side, striking the concrete off to the finished level with the screed. You will still need to float it perhaps 2 more times after that if you are going with a broom finish.

Get the rest of the concrete down, and if you are still alive, start the floating process. Use a "bull float" to get most of the surface closed up and the grout brought up, this is critical to get this right the first time!!! Setting the level properly with the screed will really make a difference too.
One more time with a hand float after an hour or so should make it ready for the broom finish.

On a slab that is 50" long you will need to run control joints or cut them in later at every 10' or so. I think it is recommended to have expansion joint every 20' but it may not be required. Again, control joints would be highly recommended..