Plot of an increasing computable function is a solvable subset of $\mathbb{N^{2}}$

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I got stuck at one of the steps of the problem's solution.

The problem is to prove that the plot of $f: \mathbb{N} \rightarrow \mathbb{N}$ (computable increasing function) is a decidable subset of $\mathbb{N^{2}}$.

My rought solution: 1) Plot is a subset $ F \subset \mathbb{N} \times \mathbb{N}$. Lets denote the following $ 1_{A \times B} {(a, b)}=1_{A}{a} \cdot 1_{B}{b}$. So, we can compute the $1_{A}{a}$, but he can we compute the $1_{B}{b}$, taking into accout that $f$ is increasing?

Thank you in advance.