Consider a relation between $X$ and $Y$ such that the area under the curve of this was proportional to the square of $Y$, what would such a graph look like.
I was inspired of this question when I was going through my Physics textbook which mentioned such a thing when discussing Current, Voltage, Resistance and it's relationships.
I couldn't find anything online, so if you could point me to some resources and similar things it'd be very nice.
$\int\limits_{x_0}^x y\,\mathrm{d}y=ky^2\Rightarrow y=2kyy'\Rightarrow y=0\hbox{ or }y'=\frac{1}{2k}\Rightarrow y=0\hbox{ or } y=\frac{x}{2k}+C$ in other words, it's an arbitrary non-vertical line.