Why would an Eadie-Hofstee Plot be non-linear?
The reason is that the inhibition models are inherently wrong.

Inhibitors bind to enzymes with the same mass action principles as substrates do so the term that should describe their binding should mirror the form of the MM equation i.e. ([S]/([S]+km)).  However all the traditional equations use (1+([I]/Ki)) rather than ([I]/([I]+ki)).  

To compound this problem the (1+([I]/Ki)) term multiplies into the Km in competitive inhibition but divides into the Vmax in the noncompetitive equation.  It is therefore not affecting these terms in the same way in these separate equations and leads to the conclusion it is upside down in the competitive equation. 

The plots above are deceiving as they allow the user to look at a linear plot and assume mechanism based on axis intercept pattern without analyzing the actual change in kinetic parameters produced by the inhibitor.  Kinetic models should be only fit using global data fitting to the proposed inhibition model.  This can be done quite easily using excel, for an example of how this can be done check out Kemmer and Keller 2010, or check youtube.

Kemmer G, Keller S. 2010. Nonlinear least-squares data fitting in Excel spreadsheets. Nature Protocols 5:267-281.

By realizing that the change in enzyme kinetic properties relates directly to inhibitor binding the logical hyperbolic shift in values exactly like the hyperbolic curve of the MM equation must be acknowledged and finite changes in the kinetic parameters must be accounted for.

i.e. Km = Km-((delta Km)*([I]/([I]+Ki)))

  Vmax = Vmax-((delta Vmax)*([I]/([I]+Ki))) 


While I have been told this may be over fitting as the competitive, noncompetitive, mixed noncompetitive equations define inhibition with one or two inhibition constant (Ki alphaKi), these terms eliminate the need for all of these equations and the family of equations that they spawned as they proved ineffective over the years (such as uncompetitive, partial competitive, partial noncompetitive, partial mixed noncompetitive, I could go on but I think you get the point).   

Additionally the competitive, noncompetitive and mixed noncompetitive equations define the effect of the inhibitor with the equilibrium binding constants and do not allow for the possibility that complete inhibition may not occur (no delta terms), leading to the family of equation to try to make up for this, i.e. partial competitive and partial noncompetitive.

Use empirical models and stop trying to force mechanistic models, the data will suggest the mechanism with good experimental design.