Linear Interpolation
Read a value between two known points off a chart or table: y = y1 + (x - x1) x (y2 - y1) / (x2 - x1), with the slope and an extrapolation flag when the query falls outside the two points (first-principles linear interpolation for derating, pump-curve, steam, psychrometric, and calibration tables).
Formula and source
y = y1 + (x - x1) x (y2 - y1) / (x2 - x1); slope = (y2 - y1) / (x2 - x1). The query is an extrapolation when x is outside [x1, x2].
Linear interpolation between two known points - first-principles linear geometry; public domain.
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