How do you call the line in the middle of a quadrant?

Question

What is the name of the line that starts at $x=0, y=0$, and goes through the following points:

$x=1, y=1$

$x=2, y=2$

$x=3, y=3$

etc?

Answer 1

There isn’t really a name for the ray you described, but a similar concept is known as the Identity line, also known as the 1:1 line or 45 degree line. The difference is because the ray you’re asking has domain $[0, \infty)$, but the identity line has domain $(-\infty, \infty)$

Answer 2

I think by far the most common name is just "the line $y=x$". (In fact, as amd's comment on another answer points out, you seem to be talking about "the line $y=x$ for $x\geq 0$".)