How to graph the equation: y = x − 2 x + 1 ?

Rewrite as $y=1-3/(x+1)$, or $(y-1)=-3/(x+1)$
This is simply the regular recriprocal equation, with the axies rescaled. The standard Y axis, representing X=0, is now marked x=-1. That is, the x-numbers are moved one to the right. The old X axis of 0,1,2,3 become -1, 0, 1, 2..
The old X axis, or Y=0 becomes y=1, and we have to rescale by a factor of 3. So the old Y coordinates 0, 1, 2, 3... become 1, -2, -5, -8...
And that's it.