Kitchen Drain Help

[Pajamas]

I'm hoping someone can offer some expert advice. After I run my kitchen sink for about 10 seconds, the water level rises and drains very slowly (over hours). I have tried a vigorous plunger to no avail. I removed the water trap (clean, no debris), and confirmed no blockage between the sink and the trap. I used a 1/4" hand powered auger and can get to about 4' before I encounter resistance. At this point I am able to auger past but after withdrawing the snake I see no signs of anything really stuck in the screw and no improvement in draining. I have attached pictures of the plumbing. I have a few questions:

1. The third and fourth image show the same bend where my drain pipe attaches to the building pipe (runs vertically but cannot be seen in the picture). This is at about 4' and I presume this is where I'm encountering resistance with the auger. Is the picture just showing a fastener or is this some sort of trap? It's in a pretty inaccessible location and I'd basically have to take apart my kitchen counter to access it.

2. I'm wondering if the auger is encountering resistance at 4' because there's a bend or if there is a blockage?

3. If there is a blockage, I wonder if it is either in my pipes at that fitting or in the building pipes but my auger is going up instead of down. Is there a better way to go about approaching this problem?

4. Am I missing something entirely?

 

[Mr_David]

If you got a hand snake to the 90 where it turns into the wall and no further, then you may have a hard deposit that the hand snake is not going to bust through. May take a motorized snake to clean it.
Best left to someone who knows how to use one.

if you're getting into the wall fitting and cable is going up, bend the end of the cable like your finger pulling a gun trigger. A hand snake is not really very efficient for clearing a kitchen drain stoppage. Some heavy and hard build ups can occur.

 

[Zeppelin5000]

I'd say use a motorized snake preferably with a drop-head, which is basically a head with a "hinge" on it so the head can bend to turn corners. I don't think you're getting past that elbow with a hand snake.

 

[SHR]

As the previous replies note, you are "missing" that you have a clogged drain pipe and you do not have the correct tool to clear it. Follow the previous poster's advice.