1. What is Linear Interpolation?

Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. It estimates values between two known values on a straight line.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

Where:

• \( (x_1, y_1) \) — First known coordinate point
• \( (x_2, y_2) \) — Second known coordinate point
• \( x \) — Input x-value between x₁ and x₂
• \( y \) — Calculated interpolated y-value

Explanation: The formula calculates the slope between two points and applies it to find the corresponding y-value for any x between them.

3. Applications of Interpolation

Details: Linear interpolation is widely used in mathematics, computer graphics, data analysis, engineering, and scientific research to estimate values between measured data points.

4. Using the Calculator

Tips: Enter two known coordinate points (x₁,y₁) and (x₂,y₂), then enter the x-value you want to interpolate. The calculator will return the corresponding y-value on the line between the two points.

5. Frequently Asked Questions (FAQ)

Q1: What if my x-value is outside the range [x₁,x₂]?
A: The calculator will still work, but this is called extrapolation rather than interpolation, and may be less accurate.

Q2: Can I use this for non-linear data?
A: Linear interpolation works best for data that is approximately linear between points. For highly non-linear data, consider other interpolation methods.

Q3: What units should I use?
A: The calculator is unit-agnostic, but all x-values must be in the same units, and all y-values must be in the same units.

Q4: Why do I get an error when x₁ = x₂?
A: When x₁ equals x₂, the denominator becomes zero, resulting in division by zero which is mathematically undefined.

Q5: How accurate is linear interpolation?
A: It's perfectly accurate for truly linear relationships. For non-linear relationships, accuracy depends on how close the points are and how non-linear the function is.