My question is an Algebraic problem

Question

 I believe what I'm about to share with you will be groundbreaking to the education of mathematics. My problem is an algebraic topic. I look up to you to solve this simple yet complicated problem.

Here it is: In illustration, think about the graph of y=x^2, the coordinate (2,4) is part of the graph but in order to locate the coordinate (2,4), one must refer to the x-coordinate 2 and then proceed to go 4 units up. What really determines whether you go left and right units or up and down units? I noticed that we all follow a rule to go up such and such units so we are forced to go up that many units but what is the principle behind that process of plotting the points on the graph. 

It seems random to locate or to plot the coordinates and to be following the rule. It may be the conventional way but there must be a solution to this problem. You might compare this problem to the definition of a point which can't be defined.Its more complicated than you think.I tried my best to make myself clear. I know I'm thinking outside the box. This problem isn't that simple. I look forward to your reply

Answer 1

every point on the graph of f(x)=y=x^2

is (x,y) = (x, f(x)) = (x, x^2) = (sqr(y), y)

for x=2, the point is (2, 2^2) = (2, f(2)) = (sqr(4), 4), = (2,4)

start at the origin and go right 2, then up f(2)