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 line or curve.

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-coordinate to interpolate
• \( y \) — The calculated y-coordinate

Explanation: The formula finds the y-value corresponding to a given x-value by assuming a straight line between the two known points.

3. Applications of Linear 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 (x,y) points and the x-value you want to interpolate. The calculator will compute the corresponding y-value on the line between your known points.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between interpolation and extrapolation?
A: Interpolation estimates values between known points, while extrapolation estimates values outside the known range (which can be less accurate).

Q2: When is linear interpolation not appropriate?
A: When the relationship between points is clearly non-linear (exponential, logarithmic, etc.), higher-order interpolation methods may be better.

Q3: Can I interpolate multiple points at once?
A: This calculator handles single-point interpolation. For multiple points, you would need to run multiple calculations.

Q4: What if my known points have the same x-value?
A: The calculation is impossible (division by zero) as it would represent a vertical line which isn't a function.

Q5: How accurate is linear interpolation?
A: It's perfectly accurate when the true relationship is linear, and reasonably accurate for small intervals even with non-linear relationships.