Linear interpolation estimates a value between two known data points by assuming the relationship between them is a straight line. It is the most reused piece of arithmetic on the FE Civil exam, because the reference handbook is full of tables that stop short of the exact value a problem needs. Steam properties, soil parameters, interest factors, and survey curve elements all get read this way. The formula is the point-slope form of a line rearranged: start at the lower known value and add the fraction of the way across the interval times the total change across it. Written out, that fraction is the difference between the target input and the lower input, divided by the width of the interval. Two habits prevent nearly every interpolation error. First, sketch or at least state which variable is the input and which is the output, because tables are printed in both orientations and inverse interpolation, solving for the input that produces a given output, uses the same formula with the roles swapped. Second, sanity-check the result against the bracket: an interpolated value must lie between the two known values. If it does not, the inputs were transposed. Extending the line beyond the two known points is extrapolation rather than interpolation, and it is far less reliable.
Commit to an answer before opening the solution. Each problem shows the governing model, every substitution, a unit check, and why each wrong choice is wrong.
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. 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.
FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES. All practice questions are original and generated for study purposes based on publicly available exam specifications.