I'm currently teaching introductory linear algebra. This is my first time as the instructor, but I have been a teaching assistant for the class before.
A recurring problem I have is drawing a clear plot of a plane that passes through the origin.
In my lecture today, I drew a plot like this (although this is cleaned up---the version in the lecture was quite bad):
Even looking at it myself, I find it difficult to parse which lines are where. I'd love to hear some advice on how to make this more clear.
For context, the equation for the plane is $$ \mathcal{P} := \{(x, y, z) \in \mathbb{R} \mid z = ax + by + c\},$$ with $a = 1/2$, $b = 1$, and $c=0$.