1. What is Linear Interpolation?

Linear interpolation is a method of estimating values between two known data points. It assumes the change between points is linear and calculates intermediate values accordingly.

2. How Does the Calculator Work?

The calculator uses the linear interpolation formula:

Where:

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

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

3. Applications of Interpolation

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

4. Using the Calculator

Tips: Enter coordinates for two known points and the x-value where you want to estimate the y-value. The x-value should typically be between x₁ and x₂ for best results.

5. Frequently Asked Questions (FAQ)

Q1: What if my x-value is outside the known points?
A: This is called extrapolation and is less reliable than interpolation, especially if the relationship isn't truly linear.

Q2: What happens if x₁ = x₂?
A: The calculation is undefined (division by zero) as it would represent a vertical line with infinite slope.

Q3: Can I use this for non-linear data?
A: Linear interpolation works best for linear relationships. For non-linear data, consider polynomial or spline interpolation.

Q4: How accurate is linear interpolation?
A: It's exact for linear relationships and provides reasonable estimates for mildly non-linear data between close points.

Q5: Can I interpolate multiple dimensions?
A: This calculator handles 2D interpolation. For higher dimensions, more complex methods like bilinear or trilinear interpolation are needed.