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 $f(x) = \frac {1}{10}x - 2$. Substituting $0$ for $x$ in this equation yields $f (0) = \dfrac{1}{10}(0) - 2$, or $f(0) = -2$. Since it's given that $y = f(x)$, it follows that $y = -2$ when $x = 0$. Therefore, the y-intercept of the graph of $y = f(x)$ 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.