Lipschitz Constant of a linear function

Question

What is the Lipschitz constant of a linear function, in the form of f(x)=ax+b

For any p,q in the domain, ||f(p)-f(q)|| = ||(ap+b) - (aq+b)|| = ||a(p-q)|| <= |a|*||p-q||

Is it a?

Answer 1

Yes. Recall that the derivative of a linear function $ax + b$ is constant ($a$), and the maximum of the derivative must be $a$ itself.