How do I represent this relationship

[frasifrasi]

So basically, I want to write a general formula for this:

(3,0)
(4,1)
(5,2)

-->meaning that whenver you increase x by 1, x also increases by 1 starting with (0,0)( iguess...).


This is to answer this question:

Carbon nanotubes with indices (n, m) that satisfy n-m=3l, where l is an integer, behave likemetals (copper, silver, aluminum, etc). The rest behave like semiconductors (silicon, germaniumetc). Can you identify at least one group of vectors that would produce metallic carbon nanotubes?Find as many as you can if you are able to.

If anyone knows of anyother group, that would be nice as well.

Thank you.

 

[symbolipoint]

Those points lie on a line. Does that help you? Are you aware that the origin does not lie on this line?

The carbon and materials for nanotubes part I do not understand; I only commented on the three given points.

 

[HallsofIvy]

(Almost) Any line can be written in the form y= ax+ b. Take (x,y) from any two of the points so you have two equations to solve for a and b. You can use the third point to check your equation.

 

[frasifrasi]

Ok, but this has nothing to do with the coordinate system. The values (n,m) are supposed to components of vectors that are not plotted on a regular 90 degree coordinate system. I just want to express the trend that (3,0), (4,1), etc such that n-m=3(integer).

Any thoughts?

 

[frasifrasi]

I guess I can just say (3 + n, n)where n is a positive integer.