Graph the all the combinations of $cu+dv$ with the restrictions of $c$ and $d$

Question

Graph the all the combinations of $cu+dv$ with the restrictions of $c$ and $d$ are integers (both positive and negative )

i draw this is it right ?

Answer 1

It should look something like this. Just replace $a_1, a_2$ with $u,v$. Since your multipliers are always integers you get a lattice like structure. What you have written is the formula for a general point in a bravis lattice in 2D with $u,v$ being the basis vectors.