Lipschitz bounds for $a\|x-y\|+b$

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During my attempt to formulate a Lipschitz bound in a course extra material, I encountered an expression in the form $a\|x-y\|+b$, with $a,b>0$. Is it possible to adjust the expression to a form of the type $C(a,b)\|x-y\|$, so that $C(a,b)$ serves as Lipschitz constant?