Two point form of solving straight line problems in coordinate geometry If we find the slope of a line via two point form we find that when the for different points in the same straight line we have different equations. Why is it so? Say, if the points were $3,5$ and $6,10$ then the equation was $2x-y=1$ and when the points were $4,6$ and $6,11$ then the equation of line was $2x-y=2$. Why this deviation?

The two st lines you mentioned are compeltely different so of course you will have two different equations  !!
For the first one passing through $ (3,5)$  and  $(6,10)$, its equation is $y=5/3x$.
For the second one passing through $ (4,6)$  and  $(6,11)$, its equation is  $ y=5/2x-4$.
Here is their plot : 
