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We analyze the expansions in terms of the approximate roots of a Weierstrasspolynomial $f$ defining a plane branch $(C,0)$, in the light of the toricembedded resolution of the branch. This leads to the definition of a class of(non equisingular) deformations of a plane branch $(C,0)$ supported on certainmonomials in the approximate roots of $f$. As a consequence we find out aKouchnirenko type formula for the Milnor number $(C,0)$. Our results provide ageometrical approach to Abhyankar's straight line conditions and itsconsequences. As an application we give an equisingularity criterion for afamily of plane curves to be equisingular to a plane branch and we express italgorithmically.

Approximate Roots, Toric Resolutions and Deformations of a Plane Branch