How would I graph the amount of times older I am than my brother? Recently I have been working with linear equations (in school) and since I and my brother's birthdays are coming up soon I started thinking; can I graph how many times older I am than him as the years go by?
I am 2 years older than my brother and I plotted the points on a graph with x being years and y being times older I am.

Now, this definitely isn't linear. And I don't know what the type of equation that describes it is called. So I just need a hand from you math masters by telling me what it's called so that I can research and learn it.
I'm just a curious boy who likes math. :) 

Let $x$ represent your age. Then your brother's age, since you're two years older, is $x-2$. Then the ratio of these, $x/(x-2)$ is how many times older you are than him $x$ years after your birth, and thus the graph you want is
$$y = \frac{x}{x-2}$$

Alternatively, you could let $x$ be your brother's age as in your post, and  thus $x+2$ would be your age. The corresponding graph you want is
$$y = \frac{x+2}{x}$$
where $x$ is the number of years after your brother was born. 

Both graphs are valid depending on your perspective and from whose birth you want to measure - the first is just the second shifted right two units. Just note that you want to only consider $x>2$ for the first graph and $x>0$ for the second graph; this is because it wouldn't make much sense to talk about the ratio before your brother was born. (There is also the assumption that you are precisely $2$ years older than your brother to be concerned about, but you can easily see how to adjust that.)

A footnote: these are what we call rational functions. More specifically, if
$$y = \frac{P(x)}{Q(x)}$$
where $P,Q$ are polynomials, $y$ is called a rational function - a ratio of polynomials. Here, both $P$ and $Q$ are linear functions. I believe I've seen such types of functions (where $P,Q$ are linear) be specifically called "fractional-linear" in my coursework, if you want to do some hunting on your own for them, but these were mostly in the context of transformations of complex numbers (something a bit above your level for the time being) so I doubt you'll learn much from searching for them. I'd focus on rational functions for your searching.
