Line Fitting Within Tolerance

$k$ points $(x_1,y_1) , (x_2,y_2), \ldots, (x_k, y_k)$ are said to **belong** to a line of slope $m$ within tolerance $D$, if there exists a line with slope $m$ that's at most **vertical** distance $D$ away from every point. Formally, there should exist $k$ other points $ (x_1,y'_1) , (x_2,y'_2)...(x_k, y'_k) $ such that: - $|y_i - y'_i| \leq D$ for every $i$; and - $y'_i = y'_j + (x_i-x_j) \cdo