Simulation
Use this page to show that the LS slope and intercept both have distributions that are approx normal if the data come from a normal linear model.
Click Take sample a few times to observe the variability in the least squares lines. Click Accumulate then take about 10 samples. (Click on any line to show the sample to which it belongs.)
Select Parameter estimates from the pop-up menu, again click Accumulate and take several samples. Observe that both the LS slope and intercept have symmetric distns, centred on β0 and β1.
Click Show Theory to display the theoretical normal distributions.