What do you call the line between (-2,0) and (0,0) in this graph?

Question

When I typed in $x^2-\dfrac{x}{y}=\dfrac2y$ on a graphing calculator,

the graph shows a horizontal segment between $(-2,0)$ and $(0,0)$. From the graph, I thought that there will be two values of $y$ when $0>x>-2$. But upon testing some numbers, there are no values that lies on that segment. How does this line formed and why it does not have a value?

Answer 1

I contacted Desmos (who owns the grapher in question), and here’s the official (and not particularly elucidating) explanation:

Thanks for sending in a link to your graph. Dividing by very small numbers when we sample sometimes lead to us magnifying tiny errors and finding spurious segments. It’s often useful to try writing things in a slightly different form and seeing whether that helps. In this case it seems to: https://www.desmos.com/calculator/kukmx1j4tp

Hope that makes sense and please let us know if you have other questions. Thanks! all the best, [redacted] & Team Desmos