Values of the response variable $y$ vary according to a normal distribution with standard deviation $\sigma$ for any value of the explanatory variable $x$.
The quantity $\sigma$ is an unknown parameter.

Repeated values of $y$ are independent of one another.

The relationship between the mean response of $y$ (denoted as $\mu_y$) and explanatory variable $x$
is a straight line given by
$\mu_y=\alpha+\beta x$ where $\alpha$ and $\beta$ are unknown parameters.