Linear Interpolation Calculator

How to Use the Linear Interpolation Calculator

Understanding the Inputs

Before utilizing the Linear Interpolation Calculator, familiarize yourself with the input fields required for calculations. Here’s a breakdown:

• x₀ (Known point 1, x-coordinate): This is the x-coordinate of the first known point. Enter a numerical value.
• y₀ (Known point 1, y-coordinate): This is the y-coordinate of the first known point. Enter a numerical value corresponding to x₀.
• x₁ (Known point 2, x-coordinate): This is the x-coordinate of the second known point. Enter a numerical value distinct from x₀.
• y₁ (Known point 2, y-coordinate): This is the y-coordinate of the second known point. Enter a numerical value corresponding to x₁.
• x (Point to interpolate): This is the x-coordinate of the point for which you want to find the corresponding y-value through interpolation. Enter the desired numerical value.

Inputting Your Data

To start using the calculator, follow these steps:

1. Enter the value for x₀ in the designated input field. This value is crucial as it represents one of the coordinates of your first known point.
2. Input the value for y₀. Ensure this corresponds to the x₀ you provided.
3. Provide a value for x₁, ensuring it is different from x₀, to represent the x-coordinate of your second known point.
4. Enter the value for y₁. This should correspond to the x₁ you input.
5. Finally, type in the value for x, the x-coordinate of the point you wish to interpolate.

Understanding the Results

Once you’ve input all necessary values, the calculator will present you with several results:

• Slope (m): This is calculated as (y₁ - y₀) / (x₁ - x₀). It represents the rate of change between your two known points and is displayed with four decimal precision.
• Interpolated y-value: The calculator computes this using the formula y₀ + ((y₁ - y₀) / (x₁ - x₀)) * (x - x₀). This value displays the estimated y-coordinate corresponding to your input x and is rounded to four decimal places.
• Linear Equation: The equation formed through the interpolation is displayed as y₀ + slope * (x - x₀). This provides the complete linear equation used for finding the interpolated y-value, formatted to four decimal places.

Conclusion

By carefully entering the known point coordinates and the target x-coordinate for interpolation, this calculator efficiently provides you with a slope, an interpolated y-value, and the respective linear equation. Ensure your inputs are accurate to receive reliable results.