Answer
Slopes have to be the same:$$m_a=m_b=m_c$$
If $A$ and $B$ are the furthest seats and $C$ is in between them. For the seats to be lined, the next equation must be fulfilled $$AB = AC+CB$$
Work Step by Step
Suppose we have $3$ points (three seats) $A, B$ and $C$. There can be at most $3$ possible lines connecting these points. Let's assume that these lines are $a, b$ and $c$ (And let $m$ be value of the slope).
These points will be laying on the same line, if and only if $$m_a=m_b=m_c$$
In case of using the Distance Formula, let $A$ and $B$ be the furthest seats and $C$ be in between them. For the seats to be lined, the next equation must be fulfilled $$AB = AC+CB$$