For real data $(x_i,y_i)$, a least-squares line $y=a+bx$ minimizes $\sum_i(y_i-a-bx_i)^2$. The design matrix has rows $(1,x_i)$, the coefficient vector is $(a,b)^T$, and the target vector contains the $y_i$. Slope and intercept are unique if the $x_i$ are not all equal.
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