Linear Interpolation

y = y_{0} + \frac{x - x _{0}}{x _{1} - x _{0}} (y_{1} - y_{0})

Straight-line interpolation between tabulated handbook values (factors, steam, steel properties, rainfall). Do not extrapolate unless the problem allows it.

$x 0, y 0$: First tabulated point
$x 1, y 1$: Second tabulated point

Step-by-step solved example

(i,F/P): (6%,1.338) and (8%,1.469). Estimate F/P at 7%.

Tabulated y vs x — interpolate along the straight segment between two stations.

1. Fraction
Halfway in i, so halfway in factor if linear in i.
$\frac{7 - 6}{8 - 6} = 0.5$
2. Interpolate
1.338+0.5(1.469−1.338)=1.4035.
$1.404$

Answer: ≈ 1.404

10 practice questions

0/10 correct

1.y(3) between (2,10) and (6,18) is

2.Extrapolation is

3.At the midpoint, y equals

4.Log interpolation is used when

5.(10,4) and (20,9): y(12) =

6.If x=x0, the formula returns

7.Bilinear interpolation needs

8.A 4-point Lagrange polynomial vs linear

9.Units of interpolated y are

10.(0,100) and (10,80): y(4) =