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Choice B is correct. The y-intercept of the graph of a function in the xy-plane is the point on the graph where $x=0$. It′s given that $f\left(x\right)=\frac{1}{10}x-2$. Substituting $0$ for $x$ in this equation yields $f\left(0\right)=\frac{1}{10}\left(0\right)-2$, or $f\left(0\right)=-2$. Since it′s given that $y=f\left(x\right)$, it follows that $y=-2$ when $x=0$. Therefore, the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane is $\left(0,-2\right)$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.