I'm not in school, and I'm not looking for any answer to any homework assignment. I have something I'm doing on my own, and I wanted to see if anyone comes up with the same formula, or close to it, as I did for the following.

Take a graph: draw a line so that $\displaystyle x=y$, which we know is a $\displaystyle 45^o$angle and a $\displaystyle 135^o$ angle from $\displaystyle (0,0)$ heading in a positive and negative direction on to infinity.

Now, let's say that the line goes to $\displaystyle (1,1)$ then $\displaystyle (2,2)$ then $\displaystyle (3,3)$ etc. What formula would also extend the line to $\displaystyle (-1,-1) $ $\displaystyle (-2,-2) $ $\displaystyle (-3,-3)$ ...ect., as the line extends positively?

In other words, you start from $\displaystyle (0,0)$ and the vectors extend positively, and negatively in proportion to each other. When the vector goes from $\displaystyle (0,0)$ to $\displaystyle (1,1)$ to $\displaystyle (2,2)$ it then extends to at the same time to $\displaystyle (-1,-1)$, $\displaystyle (-2,-2)$, etc.

I understand people have their own work and may not want to be sidetracked with this, but I do appreciate anything anyone has to suggest. My guess is this is a well-known formula, and I'm just don't know well enough to know it. Nevertheless, I want to get this simple formula down before proceeding on with my work.

Thank you very much in advance for anything.

Ed