Finding the coefficients of the block diagram
If you assume that the samples lie on a line then the current sample is related to the previous sample by
$$x[n]=x[n-1]+c\tag{1}$$
with some unknown constant $c$. If there are two past samples given, then $c$ is simply determined by the difference between these two samples:
$$c= x[n-1]-x[n-2]\tag{2}$$
Combining $(1)$ and $(2)$ gives
$$x[n]=2x[n-1]-x[n-2]\tag{3}$$