How do you describe a linear order on the plane geometrically?

[ehrenfest]

Homework Statement

Define a relation on the plane by setting (x_0, y_0) < (x_1, y_1) if either

$$y_0 - x_0^2 < y_1 - x_1^2$$, or $$y_0 - x_0^2 = y_1 - x_1^2$$ and $$x_0 < x_1$$

I showed that this is a strict linear order on the plane but then the question asks me to describe it geometrically. I am not really sure how you describe something like this geometrically. Anyone want to clarify what that means?

Homework Equations

The Attempt at a Solution

 

[morphism]

Try drawing some parabolas!