ax+by+c is the general equation of a line and the dependance between x and y is represented here
that is if we are giving a value to either x or y then we can find the value of the other variable from this equation
if any one of a,b, or c is zero,again that also will be an equation of a line
because if a=0
then equation become by+c=0
or y=-c/a
it is also an equation of line
similarly we can say what happens when b and c are zero
try to understand the concept and like if you are satisfied