# Linear-fit, how to minimize maximum error rather than average error

I have some points in 2D space and simply want to fit a line through them (solve for $m$ and $b$ of the equation $y = mx + b$) such that the maximum error for any given point is as small as possible. This is not least-squares linear regression because my goal is not to minimize the total error among all points. Instead, I want to minimize the error of the point that has the worst fit. Is there an equation for how to do this?