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
• \( x \) — The x-value for which you want to find the corresponding y-value
• \( y \) — The interpolated y-value at position x

Explanation: The formula calculates the slope between two points and uses it to estimate the y-value at any given x-position between them.

3. Applications of Linear Interpolation

Details: Linear interpolation is widely used in mathematics, computer graphics, data analysis, engineering, and scientific computing. It's particularly useful for estimating values between measured data points, creating smooth transitions in animations, and filling gaps in datasets.

4. Using the Calculator

Tips: Enter two known coordinate points (x1,y1) and (x2,y2), then enter the x-value where you want to interpolate. Ensure x2 ≠ x1 to avoid division by zero errors. All values can be any real numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens if x is outside the range [x1, x2]?
A: The formula still works mathematically, but this is called extrapolation rather than interpolation. Results may be less accurate outside the known range.

Q2: Can I use this for non-linear data?
A: Linear interpolation assumes a straight line between points. For non-linear data, other interpolation methods (quadratic, cubic spline) may be more appropriate.

Q3: What precision does the calculator provide?
A: The calculator provides results with 4 decimal places precision, suitable for most applications.

Q4: Are there any limitations to linear interpolation?
A: Linear interpolation can't capture curves or complex patterns between points. It assumes constant rate of change between known points.

Q5: Can I use negative values?
A: Yes, the calculator works with both positive and negative values for all inputs.