Plot transistor characteristics Id vs. Vds

Homework Statement

Assume the circuit pictured below:

http://img259.imageshack.us/img259/3443/problem2bwz3.jpg [Broken]

The transistor follows these rules:

$$I_D\,=\,0$$ if $$V_{GS}\,\le\,V_T$$

$$I_D\,=\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)$$ if $$V_{GS}\,\ge\,V_T\,$$ and $$\,0\,\le\,V_{DS}\,\le\,V_{DS, SAT}$$

$$I_D\,=\,g_m\,\left(V_{GS}\,-\,V_T\right)$$ if $$V_{GS}\,\ge\,V_T\,$$ and $$\,V_{DS}\,\ge\,V_{DS, SAT}$$

$$I_G\,=\,0$$ at all times

The question: Plot the transistor characteristics Id vs. Vds for Vds = 0 to 5V and Vgs = 1 to 5V in 0.25V steps.

Homework Equations

KCL, KVL, v = iR, the transistor rules above.

The Attempt at a Solution

I did KCL at node Vd and node Vs.

Vd) $$\frac{V_{out}\,-\,V_{cc}}{R_2}\,+\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)\,=\,0$$

Vs) $$\frac{V_S}{R_1}\,-\,g_m\,\left(V_{GS}\,-\,V_T\right)\,\left(\frac{V_{DS}}{V_{DS, SAT}}\right)\,=\,0$$

I don't know how these help me if I solve them for Vout ot Vs or whatever. The problem before this one had the exact same circuit diagram with different transistor rules. The previous problem did not have the last fractional term for the middle region of operation for the transistor. This made a graph that looked like this:

http://img264.imageshack.us/img264/5963/homework5problem1aeg7.jpg [Broken]

However, I know that the same graph for these new transistor rules is not just straight lines again. Each line in this new graph of Id vs. Vds is supposed to start out at the origin and linearly slope upwards to the straight lines in the graph from the previous problem (above). The problem is that I don't know what to graph or how to go about getting the equations for it. Please help!

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