🧱 See It
Interpolation means estimating a value BETWEEN two known data points. Extrapolation means estimating a value BEYOND the known data — before the first point or after the last one. Interpolation is generally safer, since it's surrounded by real, recorded data on both sides. Extrapolation assumes the same pattern keeps going exactly the same way outside that range, which isn't always true.
✏️ Draw It
The same y = 60x distance graph, now extended. The line stays SOLID across the recorded range (0 to 3 hours), then turns DASHED beyond it — a visual signal that this part is less certain:
The open circle on the solid line (1.5 hours) is an interpolated estimate — safely inside known data. The open circle on the dashed line (4 hours) is an extrapolated estimate — same calculation, but the surrounding line style shows it's less certain.
🔢 Write It
The exact same rule computes both kinds of estimate — only the confidence differs:
y = 60x
Interpolated (inside the known 0–3 hour range): x = 1.5 → y = 60 × 1.5 = 90 km
Extrapolated (beyond the known range): x = 10 → y = 60 × 10 = 600 km
💡 Worked Examples
Example 1 — Interpolate: estimate the distance at x = 1.5 hours (between the known x = 1 and x = 2 data points)
- Use the rule:
y = 60x - Substitute:
y = 60 × 1.5 - Answer:
y = 90 km— safe, since it sits between two recorded points.
Example 2 — Extrapolate: estimate the distance at x = 10 hours (well beyond the recorded 0–3 hour range)
- Use the rule:
y = 60x - Substitute:
y = 60 × 10 - Answer:
y = 600 km— but this assumes the car keeps going at exactly 60 km/h for the entire 10 hours, with no stops, no traffic, no rest breaks. That's a much shakier assumption than the interpolated estimate, so this number deserves far less confidence even though the arithmetic is just as simple.