Two-Point Linear interpolation The equation of the line through (x_1, y_1) and (
ID: 3009799 • Letter: T
Question
Two-Point Linear interpolation The equation of the line through (x_1, y_1) and (x_2, y_2) on a plot of y versus x is y = y_1 + x - x_1/x_2 - x_1 (y_2 - y_1) (Can you prove it?) You may use this equation to estimate y for an x between x_1 and x_2; you may also use it to estimate y for an x outside of this range (i.c., to extrapolate the data), but with a much greater risk of inaccuracy. If the points in a table are relatively close together, linear interpolation should provide an accurate estimate of y for any x and vice versa; on the other hand, if the points are widely separated or if the data are to be extrapolated, one of the curve-fitting techniques to be outlined in the next section should be used. Values of a variable (f) are measured at several times (t): Show that if two-point linear interpolation is used f(t = 1.3) 1.9; f(f = 5) 2.25.Explanation / Answer
(t,f ) - (1,1) (2,4), (3,8)
f(1.3) = f(1) + (4-1)/(2-1) (1.3-1)
= 1+3*0.3 = 1.9
b)t(5) = t(4) + (3-2)/(8-4)*(5-4)
=2+1/4=2.25
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