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:

• \( (x1, y1) \) — First known point coordinates
• \( (x2, y2) \) — Second known point coordinates
• \( x \) — Input x-value for interpolation
• \( y \) — Calculated interpolated y-value

Explanation: The formula calculates the y-value corresponding to a given x-value by assuming a linear relationship between the two known data points.

3. Applications of Linear Interpolation

Details: Linear interpolation is widely used in mathematics, computer graphics, data analysis, engineering, and scientific computing for estimating values between known data points, creating smooth transitions, and filling missing data.

4. Using the Calculator

Tips: Enter two known data points (x1,y1) and (x2,y2), and the x-value for which you want to find the corresponding y-value. Ensure x1 and x2 are different to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between interpolation and extrapolation?
A: Interpolation estimates values within the range of known data points, while extrapolation estimates values outside this range.

Q2: When is linear interpolation not appropriate?
A: When the relationship between data points is non-linear or when higher precision is required for complex curves.

Q3: Can I use this for more than two data points?
A: This calculator handles two points. For multiple points, piecewise linear interpolation or other methods would be needed.

Q4: What if my x-value is outside the range [x1, x2]?
A: The calculator will still compute the result, but this becomes extrapolation rather than interpolation.

Q5: How accurate is linear interpolation?
A: Accuracy depends on how linear the actual relationship is between the known data points. It provides exact results for truly linear relationships.