Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
EASYlinear interpolation
Linear Interpolation: FE Civil practice problem 1
For the Oak Point water storage yard, a civil analyst preparing an agency resubmittal package linearly interpolates between (17, 77) and (26, 132). What value corresponds to x = 20.6?
- A61.04
- B99.00
- C72.44
- D112.02
Show the answer and worked solution
Answer: B — 99.00
Worked solution
- Step 1. Use linear interpolation
y = y1 + (x - x1)(y2 - y1)/(x2 - x1)
- Step 2. Substitute values
y = 77 + (20.6 - 17)(132 - 77)/(26 - 17) = 99
Why the other choices are wrong
- Choice A
- Working the straight-line interpolation the correct way, adding y1 to (x - x1) times the slope (y2 - y1)/(x2 - x1), produces 99.00 for the endpoints (17, 77) and (26, 132) at x = 20.6, a result that does not match 143.55 under any single documented substitution error.
- Choice C
- This 116.82 figure does not reduce to a single traceable arithmetic slip in the interpolation formula; recomputing directly gives y = 77 + (20.6 - 17)*(132 - 77)/(26 - 17) = 99.00, and neither a swapped-endpoint nor a midpoint-average substitution returns 116.82 for these coordinates.
- Choice D
- No standard interpolation substitution using the stated endpoints (17, 77) and (26, 132) at x = 20.6 lands on 77.22, so this option cannot be tied to one specific calculation mistake; the verified straight-line result is y = 77 + (20.6 - 17)*(132 - 77)/(26 - 17) = 99.00.