Information theoretic message authentication code (MAC) Let's $\ a,b\ $ be two (pseudo)random independent values, and $m$ be a message, where $a,b,m \in \mathtt{F}_p$, where $p$ is a large prime number. 



Question 1: Is $\ am+b\ $ an information theoretic MAC?

if yes 

Question 2: Is there any paper/textbook uses it?
Just collecting some of the comments, if you make sure that $a$ and $b$ are chosen uniformly at random with $a \neq 0 \mod p$, then the given function is a information-theoretic MAC, basically because it satisfies the following property:


  If $h_k(m) = am + b$ with $k= (a,b)$ and $\tau$ is the codomain of $h_k$, then for all $m\neq m'$ and $t,t'\in\tau$ we have
  $$\operatorname{Pr}[h_k(m) = t \ \wedge\ h_k(m') = t'] = \frac{1}{|\tau|^2}$$
  (probability taken over random choice of $k$) 


When a function satisfy this property we say it is a strongly universal function, and the main result is that such a function is a $1/|\tau| -$secure MAC, that is, the advantage of an attacker is at most $1/|\tau|$ (notice we can not ask for this advantage to be zero because any adversary can always try to guess a valid tag).