Using linear least squares to fit a line given some samples

Samples are $(x_i, y_i)$ pairs. To find a line $y = mx + c$ that fits them best we form matrices A and b where

$A = \begin{bmatrix} x_1 & 1 \\ x_2 & 1 \\ ... \\ x_n & 1 \end{bmatrix} $ $fit = \begin{bmatrix} m \\ c \end{bmatrix}$ $b = \begin{bmatrix} y_1 \\ y_2 \\ ... \\ y_n \end{bmatrix}$

$A * fit = b$

$fit = (A^TA)^{-1}(A^Tb)$