Learning machine learning? Try my machine learning flashcards or Machine Learning with Python Cookbook.

# Linear Interpolation

Linear interpolation is used when we want to calculate a value between two points.

Imagine we want to calculate some point, $(x, y)$ that is between two other points $(x_1, y_1)$ and $(x_2, y_2)$. To do this, we first select some value $x$ value (often halfway between $x_2$ and $x_1$ on the x-axis) and then calculate $x$’s corresponding $y$ value using the following formula:

$$y = y_1 + \frac{y_2 - y_1}{x_2 - x_1} * (x-x_1)$$

## Create Two Coordinates

```
# Coordinates for x_1 and y_1
x1 = 0
y1 = 0
# Coordinates for x_2 and y_2
x2 = 10
y2 = 100
```

## Select x Value

```
# Select an x value half way between x2 and x1 on the x-axis
x = ((x2 - x1)/2) + x1
# View x
x
```

```
5.0
```

## Create Function For Linear Interpolation

```
# Create a function
def interpolate_y(x, x1, y1, x2, y2):
# Linear interpolation formula
y = y1 + ((y2 - y1)/(x2 - x1)) * (x - x1)
# Return y
return y
```

## Calculate y

```
# Interpolate y
y = interpolate_y(x, x1, y1, x2, y2)
```

## Print x

`x`

```
5.0
```

## Print y

`y`

```
50.0
```