Linear interpolation is a method for estimating a value between two known data points by assuming the relationship is linear. Given two points (x₀, y₀) and (x₁, y₁), interpolation finds the y-value for any x between them using the formula: y = y₀ + (y₁ − y₀) × (x − x₀) / (x₁ − x₀). This straightforward technique is widely used in computer graphics, data analysis, and engineering to estimate missing values, smooth curves, and create transitions between known data points. When x falls outside the range [x₀, x₁], the method becomes extrapolation, which is generally less reliable but still mathematically valid.

Linear interpolation is foundational in countless applications: animation systems use it to transition values over time, geographic information systems interpolate elevation data, engineers use it to estimate material properties, and scientists apply it to convert between measurement scales. The method assumes a perfectly linear relationship, so it works best when the underlying data is actually linear or nearly so. For curved or nonlinear data, more sophisticated interpolation methods like polynomial or spline interpolation may provide better accuracy, but linear interpolation remains the go-to choice for simplicity, speed, and when data is genuinely linear.