SME
Numerical Methods for Engineers · Problem type
Linear interpolation in a table
Use this for “A table lists y = 2676 at x = 100 and y = 2776 at x = 150. Estimate y at x = 120.”
Chart
f(120) = 2,716
Ringed: the nodes (100, 2,676), (150, 2,776)
This is an example. Type your own values to start a new problem.
s
=
−
−
y
=
y₁
+
s
×
(
x
−
x₁
)
Formulas
s
=
y₂
−
y₁
x₂
−
x₁
2
=
2,776 − 2,676
150 − 100
y
=
y₁
+
(
x
−
x₁
)
×
s
2,716 = 2,676 + (120 − 100) × 2
Assumptions
•
Between two neighbouring table rows the values are taken to change along a straight line.
•
Pick the two rows that bracket x, so the estimate interpolates rather than extrapolates.
•
Typing y instead reads the table backward for x (inverse interpolation).
Step-by-step
WE KNOW
x = 120, x₁ = 100, y₁ = 2,676, x₂ = 150, y₂ = 2,776
FIND
slope between rows (s), estimated value (y)
Step 1 · Find slope between rows (s)
Use s = (y₂ − y₁) ÷ (x₂ − x₁)
Rise
over
run
between
the
two
rows:
how
much
y
changes
for
each
unit
of
x
.
s
=
2,776 − 2,676
150 − 100
s
=
100
50
s
=
2
Step 2 · Find estimated value (y)
Use y = y₁ + (x − x₁) × s
Start
at
the
lower
row
and
climb
the
line
for
the
distance
x
−
x₁
.
y
=
2,676
+
(120
−
100)
×
2
y
=
2,676
+
20
×
2
y
=
2,676
+
40
y
=
2,716
Check
Put the numbers back in. Both sides should match.
2
=
2,776 − 2,676
150 − 100
✓
2,716 = 2,676 + (120 − 100) × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.