The following is Linear Interpolation Formulay=y1+(x−x1)(x2−x1)×(y2−y1) The La-grange’s Interpolation Formula is given as,y=(x−x1)(x−x2)……(x−xn)(xo−x1)(x0−x2)….(x0−−xn)y+(x−x0)(x−xn)….(x−xn)(x1−x0)(x1−x2….((x1−xn)y1+(x−x1)(x−x2)….(x−xn)(xo−x1)(x0−x2)…..(xo−xn)yn Some solved problems on interpolation are given below: Solved Examples Question 1: Using the interpolation formula, find the value of y at x = 8 given some set of values (2, 6), (5, 9) ?Solution:The known values are,x0=8,x1=2,x2=5,y1=6,y2=9 y=y1+(x−x1)(x2−x1)×(y2−y1) y=6+((8−2)(5−2)×(9−6)y = 6 + 6y = 12