MOSFET load line - VGS above VDD?
The instructor made what is -- in my opinion -- a poor choice of voltages to use in his example.  In a MOSFET there's real constraints on \$v_{gs}\$ that pertain to \$V_{DD}\$, or even to \$v_d\$.  The situation's different for a JFET -- but we're not talking about JFETs here.
Each of the traces in the set of characteristic curves for the MOSFET (the plot on the left) are a function of the drain voltage (\$v_d\$), the characteristics of the FET, and the gate-source voltage (\$v_{gs}\$).  They have nothing at all to do with whatever \$V_{DD}\$ may happen to be.
In fact, \$V_{DD}\$ is just the voltage of the drain supply.  The FET does not &quot;know&quot; what it is -- the FET only responds to the voltages and currents on its pins.

Does the MOSFET break?

There is a maximum \$v_{gs}\$ value.  It's typically around 20V for most power MOSFETs today (RF MOSFETS may be wimpier).  But it has nothing directly to do with \$V_{DD}\$.

or is there some equation that governs it's Vds and iD at these given values for Vgs?
Is there an equation for this behaviour?

Yes and no.  With a set \$v_{gs}\$, the drain and source terminal pair act like any other two-terminal device; i.e., there's a fixed relationship between \$v_{ds}\$ and the drain (and source) current.  You can never control voltage and current independently on a two-terminal device of fixed characteristics.
Having said that, there most certainly are equations that describe how \$i_d\$ will behave as a function of \$v_{ds}\$ and \$v_{gs}\$.  The easiest place that I can point you to is Wikipedia, but it's in innumerable circuit design textbooks (usually starting with 2nd- or 3rd- year circuit design; it's been long enough I can't remember which one!!).
https://en.wikipedia.org/wiki/MOSFET#Modes_of_operation