A linear biochemical pathway is a chain of enzyme-catalyzed reaction steps. The figure below shows a three step pathway, with intermediates,  and . In order to sustain a steady-state, the boundary species  and  are fixed.
At steady-state the rate of reaction is the same at each step. This means there is an overall flux from X_o to X_1.
Linear pathways possess some well-known properties:
# Flux control is biased towards the first few steps of the pathway. Flux control shifts more to the first step as the equilibrium constants become large. 
# Flux control is small at reactions close to equilibrium.
# Assuming reversibly, flux control at a given step is proportional to the product of the equilibrium constants. For example, flux control at the second step in a three step pathway is proportional to the product of the second and third equilibrium constants.
In all cases, a rationale for these behaviors is given in terms of how elasticities transmit changes through a pathway.