Conditional Interpretations of Linear Regression

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We estimate a linear regressor in the 1 dimensional with x and y random variables with zero mean:

y/x = $\alpha$ x

We can rewrite this using the variance of the variables as: y/x = $\rho \frac{\sigma_y}{\sigma_x}$x

What can we say about x/y?

Looking at this deterministic, $\alpha$ is the rate of change of y w.r.t. x. So we could say that we x = $\frac{1}{\alpha}$y.

Can we say anything more concretely?