Implicit differentiation and inverse trigonometric functions practice question 20

What does parallel to $y = \tfrac{1}{2}x$ say about the slope of a tangent? At which points does $\arctan x$ have that slope?

Parallel means the same slope, and the slope of $\arctan x$ is $\dfrac{1}{1 + x^{2}}$. Solve $\dfrac{1}{1 + x^{2}} = \dfrac{1}{2}$.

At the point with $x < 0$, write the tangent line in point-slope form and set $x = 0$.