Is it possible to formulate any line or curve in 2d space ?! I wonder how we can explain any kind of lines or curves as a formula!
more clear,can we say that "any kind of lines or curves have a formula but we cannot find their formula"?!
 A: It makes no sense just to say if you have a line or curve, can you find a function or relation to represent it. Most people would take a line or curve to mean you already have a function or relation you are using to describe them. If you mean if you were to draw some kind of 'curve' or sketch on a piece of graph paper, could you find a function or relation to represent it. Then the answer is a definite maybe. Let me explain.
The naive answer is that you could merely write down a rule $f(x)=y$ for every point $(x,y)$ on the graph. But in practice you'd have to write an uncountable infinite amount of points--impractical. So on to the more practical answer:
Most shapes you could draw on a sheet of paper could be easily put into the form of $f(x)=$ something or $f(y)=$ something or maybe something in a parametric form $x(t)=$ something $y(t)=$ something. Examples would be lines, polynomial-like curves, trig-like curves, circles, et cetera. Or you could use equations similar to how we define elliptic curves. For functions which are 'smooth', we can approximate them using polynomials (this is Taylor's Theorem). 
Then we have uglier functions like
$$
f(x)=
\begin{cases}
x, \text{ if } x \in \mathbb{Q} \\
0, \text{ if }x \in \mathbb{Q}^C
\end{cases}
$$
Then again, one might say these aren't included in your answer as no human could draw it. In any case, even for this nasty, impossible to graph function, we have a function above to describe it. Think of the graph as a set of numbers, then using the same type of constructions used in constructing Lebesgue measurable functions, we should be able to find some type of approximation that will fit the function just fine (though it won't be pretty) in the sense it converges to the graph you would have drawn. 
However, this just covers 'most' things you would draw in the plane. There are an infinite amount of things that one could draw. So I certainly don't know if there exists things you could at least find a relation for. If there were to be such things, they would be very odd indeed and I doubt they would fit your criterion of being able to be drawn by a human. 
In any case, even the oddest functions you could imagine can be given piecewise relations that construct them. A absolutely stunning example of this was given using Mathematica on the Mathematica blog. I suggest you check these out as they are probably the perfect example of what you were looking for:
Making Formulas for Everything — From Pi to the Pink Panther to Sir Isaac Newton
Even More Formulas for Everything — From Filled Algebraic Curves to the Twitter Bird, the American Flag, Chocolate Easter Bunnies, and the Superman Solid
