Can we know the equation of line " $L$ " from one point $P(a,b)$ in this line?

Question

Suppose we have a point $ p(a,b)$ a and b are given and let $L$ be a line s.t $p(a,b) $ belong to $L$ By this information can we know the equation of L in terms of $P(a.b)$ ?can it gives as more information about $ L$?

Answer 1

If we just have one point $p(a,b)$ known then there are $\text{infinitely (uncountably) many }$ straight lines passing through it. We have to know at least two points to identify the equation of a line. See Euclid's first postulate here and here

Answer 2

"Suppose we have a point p(a,b) a and b are given and let L be a line s.t p(a,b) belong to L By this information can we know the equation of L in terms of P(a.b) ?can it gives as more information about L?" I'm not sure I understand this. You say "p(a, b)" is a point but what are a and b? Do you mean that p is a "point valued function of a and b"? If a and b are independent variables, then p(a, b) will, in general, be two dimensional, a plane, not a line.