Linear equations are defined as those that do not include roots of variables. The discussion centers on whether specific equations labeled as (a) and (f) qualify as linear, with a particular focus on the presence of the term $-\sqrt{2x_3}$. One participant suggests that this term may be a typo and should instead be written as $-\sqrt{2} \hspace{1 mm} x_3$ to meet linearity criteria. The conversation emphasizes the importance of correctly identifying the form of equations to determine their linearity. Accurate representation of variables is crucial in classifying equations as linear.
