If $S_{xx}=\sum_i(x_i-\bar x)^2>0$, the fitted slope is $b=\sum_i(x_i-\bar x)(y_i-\bar y)/S_{xx}$ and $a=\bar y-b\bar x$. For $(0,1),(1,2),(2,2)$, $\bar x=1$, $\bar y=5/3$, $b=1/2$, and $a=7/6$. If $S_{xx}=0$, slope is not identifiable.
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