Language of the graph of an affine function
Hint:

$53 \cdot 100000010000000000 + 4 = 5300000530000000004$.

Sketch:


   Assume $a$ has $n$ digits and $b$ has $m$ digits.

 If $\overline{x}=10^k \underbrace{00\dots01}_{n}0^l\underbrace{00\dots0}_{m}$ for some $k,l$ then

 $\overline{ax+b}=\overline{a}0^k \overline{a} 0^l \overline{b}$.

 If $L$ was context-free, then
 
 $$L&#39;=L \cap 10^{\ast}0^{n-1}10^{\ast}0^m \mathtt: (0+1+2+...+9)^{\ast} = \{10^{k+n-1}10^{l+m} \mathtt: \overline{a}0^k\overline{a}0^l\overline{b}:k,l \in \mathbb N\}$$
 would be context-free as well.
 
 Given a PDA $M$ for $L&#39;$ we could construct a PDA $N$ for $\{a^n b^m c^n d^m\}$ , a well-known non-context-free language. $N$ simulates $M$, but it is "feeding" different letters; it is a composition of $M$ with a transducer. Initially, $N$ behaves as if $M$ read $1$. Then, consecutive $a$'s are interpreted as $0$'s. Next, $N$ behaves as if $M$ read $0^{n-1}1$, and treats consecutive $b$'s as $0$'s, then as if it read $0^m \mathtt: \overline{a}$ etc.