Simple math plotting question

[Psy_Mike]

So this is extremely simple, but I don't have the literature to read up on and it seems hard to find this question by googling. So sorry if it's too simple!

Say we have a function z which depends on 2 variables, x and y (say z=x-y for the sake of.. something)

If we would like to plot this we would get 3 dimensions, x y and z. What if me make, for example x, exogenous? Would we still want to plot this in 3 dimensions? It should be possible to plot it in 2 dimensions yes? But what is the mathematically "correct" way to do it?

Instinctively I'd still figure there will be 3 dimensions where there . But if it's not, do we just view x (in this case) as a constant in a 2d plot like z=c+y? So when x varies it only changes the intercept of the z axis?

Sorry again since this is ridiculously simple..

Thanks!

[mickeyg13]

If I understand your question correctly, you can start by considering it in the 2D case. These represent the cross sections of the 3D graph. So in the example of z=c+y, with c a constant, then in the 2D graph that would obviously be a line of slope 1 with z-intercept of c. Since x does not affect this graph, these types of cross sections will always be the same. So in a sense, you are taking the 2D case and sliding it through all possible values of x, in this case resulting in a plane in 3-space.

If you instead had, for example, y^2 + z^2 = 1, then the cross sections are circles of radius 1 centered at the origin, but this occurs for all values of x, so the result is a cylinder. I hope that made sense/answered your question.

[Psy_Mike]

Aah ya that makes sense.

So I will still be plotting this in a 3 dimensional space, and will have the same zy plane for all x then yes? So graphically this would look like a linear plane with a constant slope going through all x?

Thanks a lot mickey!

[Psy_Mike]

Sorry for bringing this back up..

Does anyone know a good plotting program where you can assign exogenous variable and stuff so I can get a good feel for how this works? I'm still a bit confused how, for example, a z=x^2+y with 'normal' variables graph differs from a z=x^2+y with x as an exogenous variable.