How does Wien's Scaling Law unify experimental data in blackbody radiation?

[Narcol2000]

How does Wien's scaling law

$$\frac{u(\lambda)}{T^5} = \frac{f(\lambda T)}{\lambda^5T^5}$$

imply that if $$\frac{u(\lambda)}{T^5}$$ is plotted as a function of $$\lambda T$$, all experimental data will lie on a single curve?

 

[CompuChip]

I don't know anything about the physics here, but it seems obvious to me that if you plot $$y = u(\lambda)/T^5$$ versus $$x = \lambda T$$ then Wien's scaling law tells you that $$y = f(x) / x^5$$. So if you take a data point (x', y') and Wiens' law is true, then y' should be (within error) f(x')/(x')^5.