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:  

\[
E + S \rightleftharpoons ES \rightarrow E + _____ _________ _______ _______ ___ __________ ____.
______ _________ _____ ___ ______ ___ _____ ________ _______.
________ ____ _______ __________ ___ _________ ______.
________ ___ ________ ____ ______ ____ _________ ____ ______ ____ _______ ___.
________ _________ ________ __________ _______ _______ ______.
_____ ____ _____ _________ ____ _______ ___ ___ ______.
_________ ____ ________ _______ ________ ____ _______ __________ ______.
__________ _________ _____ ________ _________ __________ ___.
_______ ____ ____ _________ __________ ______ _____.
__________ __________ _________ _____ __________ _________ _____.
__________ _________ ___ ____ ____ ______ ______ _______ ______.
__________ ____ _______ _______ ______ _________ _________.
__________ _______ ___ __________ ______ ______ _______ _______ _________ ______ ________.
_____ ___ ______ ______ ____ ___ _________ ___.
_________ ___ ______ ________ _______ _____.
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