Modified Formula for the Slope

  The formula for the slope in the last blog assumed that Δt_k = t_k - t₈₀₄ so that Δt₀ = 0. The formula can be modified to give the best slope through an arbitrary point (t_p,ΔT_p) is as follows.

This vector formula is similar to method used to estimate the derivative of f(t) using Δf/Δt. The dot products are needed since division is not defined for vectors.