Fit regression model from a fan-shaped relation, in R I get a fan-shaped scatter plot of the relation between two different quantitative variables:

I am trying to fit a linear model for this relation. I think I should apply some kind of transformation to the variables in order to unify the ascent variance in the relation before fitting a linear regression model, but I can't find the way to do it. Or maybe, there is a better model to use in these cases, I can't either find it.
I have tried rlm, but the residuals still have heteroscedasticity. I have also tried to apply a SD ratio calculated from all the y of each x and other similar erratic approaches.
My questions:


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*Is there any typical way of fitting a model for a fan-shaped relation or a typical model to use in these cases?

*Is there any typical transformation that could be applied to the variables in order to reduce its variance?

 A: Here's two fan-shaped plots generated by different methods:

(Click here for a larger version.)
These in turn suggest two different approaches for modelling data that looks more or less like this:


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*Take logs, and fit a linear model with the coefficient restricted to 1 (also called an offset)

*divide $y$ by $x$ and then fit a constant-only model.
There will be other ways to generate data like this, and other ways to fit data like this. For example, some other possibilities are: 


*fit a gamma glm with identity link (and perhaps without an intercept)

*since the variance is proportional to $x^2$, use this fact to construct a weighted regression using weights proportional to $1/x^2$. [For a simple straight line through the origin, this should give the same result as 2.]
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[AndyW's comment about a possible missing covariate is important. However, I'm just going to deal with the question of modelling fan-shaped relationships since it's an interesting topic on its own; in practice you would want to investigate his suggestion that there appears to be potential missing covariates as well.]
