Hi, given an equation of a line of the form $\displaystyle a\times x+b\times y+c$, how can one determine if it passes through any point or not?

E.g

$\displaystyle 2\times x+3\times y=4 $ passes through some lattice point while

$\displaystyle 6\times x+8\times y=25$doesn't.

Thanks.

Ok, i think i got it, it's a Diopthene equation , and we need to check if c is a multiple of gcd(a,b) right?