How many paths through which charge can flow would be shown in a circuit diagram of series circuit?

A "series" electrical circuit has exactly one (1) path for all the current
that flows in the circuit. 

That tells us that ...

-- the current for every component in a series circuit has to flow through
all of the components;

-- if any one component is removed from a series circuit, the current stops,
and all of the components stop working;

-- the amount of current flowing past a point is the same at all points in a
series circuit.

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.