How to Find Intervals for α and β in a Linear Model Given y and x?

[zli034]

For a simple linear model:
$\alpha+\beta\times x=y$

If it is observed that $y \in (-8.51,23.20)$ given $x=4$

The question is to give intervals of $\alpha, \beta$, which satisfy $y \in (-8.51,23.20)$ given $x=4$.

Is this problem identifiable? Can it be found the unique intervals for $\alpha, \beta$?

I am guessing this is not a well defined problem. How to improve on this?

 

[mathman]

α and β are connected by a linear equation. This means the you can give any value for one variable and get an interval for the other. To improve you need another relation.