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 4
For the Mill Creek water storage yard, a materials reviewer preparing a permit comment response linearly interpolates between (14, 62) and (26, 117). What value corresponds to x = 18.8?
- A58.13
- B84.00
- C61.61
- D74.54
Show the answer and worked solution
Answer: B — 84.00
Worked solution
- Step 1. Use linear interpolation
y = y1 + (x - x1)(y2 - y1)/(x2 - x1)
- Step 2. Substitute values
y = 62 + (18.8 - 14)(117 - 62)/(26 - 14) = 84
Why the other choices are wrong
- Choice A
- This total overshoots the correctly interpolated value for x = 18.8 between the points (14, 62) and (26, 117) by more than one traceable arithmetic misstep would produce; the reliable fix is to compute (x - x1), (y2 - y1), and (x2 - x1) separately and combine them in y = y1 + (x - x1) * (y2 - y1) / (x2 - x1).
- Choice C
- This total sits above the correctly interpolated value for x = 18.8 between the points (14, 62) and (26, 117) without tracing to one clean formula slip such as swapping which endpoint anchors the calculation; reapply y = y1 + (x - x1) * (y2 - y1) / (x2 - x1) and confirm the fraction (x - x1) / (x2 - x1) before scaling the rise (y2 - y1).
- Choice D
- This total sits below the correctly interpolated value for x = 18.8 between the points (14, 62) and (26, 117); it does not match a single clean arithmetic slip in y = y1 + (x - x1) * (y2 - y1) / (x2 - x1), so recompute the fraction (x - x1) / (x2 - x1) and the rise (y2 - y1) separately before adding the product to 62.