🧠 Understanding Linear Interpolation
Linear interpolation is a mathematical method used to estimate values between two known points on a straight line. It’s commonly used in engineering, finance, data science, and even in real-world measurements where data points are limited but estimations are needed.
The key idea? If you know the value of a function at two points, say at \(x_1\) and \(x_2\), you can estimate the value at a point in between, \(x\), assuming the change is linear (in a straight line) between the two.
🧮 The Formula
Given two points \((x_1, y_1)\) and \((x_2, y_2)\), the value \(y\) at any point \(x\) between \(x_1\) and \(x_2\) is:
\[
y = y_1 + \frac{(x – x_1)}{(x_2 – x_1)} \cdot (y_2 – y_1)
\]
This formula is derived from the equation of a straight line.
📌 Example sa Tunay na Buhay
Halimbawa:
May timetable ka ng temperatura tuwing 12 PM at 2 PM:
- 12 PM → 30°C
- 2 PM → 34°C
Tinanong ka, “Ilang degrees kaya noong 1:15 PM?”
Gamit ang linear interpolation, puwede nating tantyahin ang temperatura:
- Convert time into numbers:
- 12 PM = 12.00
- 1:15 PM = 13.25
- 2 PM = 14.00
- Apply the formula:
\[
y = 30 + \frac{(13.25 – 12)}{(14 – 12)} \cdot (34 – 30) = 30 + 0.625 \cdot 4 = 30 + 2.5 = 32.5^\circ C
\]
So ang tantyang temperatura noong 1:15 PM ay 32.5°C.
🔧 Kailan Ginagamit ang Linear Interpolation?
- Pag nag-e-estimate ng temperatura, presyo, o bilis sa pagitan ng dalawang measurements.
- Sa computer graphics, ginagamit ito para i-blend ang colors o mag-transition sa animations.
- Sa engineering, ginagamit ito para kunin ang approximate values sa mga lookup tables.
🛑 Limitasyon
Linear interpolation works best only when the change between the points is fairly straight or linear. Kung curve ang data mo (like exponential or sinusoidal), this may lead to error. For better accuracy, other interpolation methods like quadratic or spline interpolation might be used.
✅ Summary
Linear interpolation is a simple but powerful tool to estimate unknown values between two known points. Just make sure the data behaves linearly in that range. Madali lang tandaan, at madali ring gamitin lalo na kung kulang ang data pero kailangan ng estimate.
