Trouble determining the correct direction errors for nullclines

[abacus]

I have a simple question regarding nullclines, as I'm having trouble determining the correct direction errors.

For example, here's a system of equations:

dx/dt = 2-x-y

dy/dt=y-x^2

x-null is y= -x + 2
y-null is y= x^2

x-null is vertical, y-null goes horizontal.

But when I divide the graph in different sections, and pick different plot points which equations do I plug into to find directions?

I know that wasn't clear, but for example:

If I want to know if on the y-null if the direction of a certain section is pointing left or right, would I plug the points I chose in:

A) dy/dt = y-X^2
B) dx/dt=2-x-y

or C) y=x^2

I'm not sure which equation to plug it in. I've tried to think it out, but I end up always confusing myself. Please point me in the right direction. Thanks.

 

[HallsofIvy]

If I understand correctly what you are doing, away from the "null clines" (pointswhere they intersect are equilibrium points) you would calculate dx/dt and dy/dt at the point then divide (dy/dt)/(dx/dt) to get the slope.

 

[abacus]

I'm not sure if that quite helps, I want to know when I take some sample points, which equations do I plug them into in order to get the correct direction.

 

[HallsofIvy]

If that is not given by the slope, (dy/dt)/(dx/dt) then I don't know what you want.