Derive the mathematical rate expression for competitive enzyme inhibition and give the graphical representation of Lineweaver-Burk plot.

In competitive enzyme inhibition, an inhibitor (I) competes with the substrate (S) for binding at the active site of the enzyme (E). The reaction mechanism can be represented as:  

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________ ____ ________ _______ ___ _________ ________ _________ ____ ___.
___ _______ _______ ________ ___ ________ _______ ________ ___ __________ _______ _______.
___ _______ ____ __________ _________ ________.
______ ___ ______ __________ ________ __________ _____ _____ _________ _______.
______ _____ ___ _________ ____ ____ _______ _______ _________ ________ ______.
______ _________ ______ ___ ________ _________ ___ ________ __________ _________ ____ ____.
___ __________ ________ ______ ___ ______ ____ ______ _____.
_______ ______ _________ __________ ___ _____ ____.
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__________ ________ _______ ________ ________ _________ __________ _______ ___ _________.
_______ ___ ________ ________ ______ _____ _________ __________ _______.
_____ __________ _____ ______ ____ ____.
____ __________ ___ _______ ____ __________ ______ _____ __________.
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