**Linear interpolation** is the process of estimating an unknown value of a function between two known values.

Given two known values (x_{1}, y_{1}) and (x_{2}, y_{2}), we can estimate the y-value for some point x by using the following formula:

y = y_{1} + (x-x_{1})(y_{2}-y_{1})/(x_{2}-x_{1})

We can use the following basic syntax to perform linear interpolation in Python:

import scipy.interpolate y_interp = scipy.interpolate.interp1d(x, y) #find y-value associated with x-value of 13 print(y_interp(13))

The following example shows how to use this syntax in practice.

**Example: Linear Interpolation in Python**

Suppose we have the following two lists of values in Python:

x = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] y = [4, 7, 11, 16, 22, 29, 38, 49, 63, 80]

We can create a quick plot x vs. y:

import matplotlib.pyplot as plt #create plot of x vs. y plt.plot(x, y, '-ob')

Now suppose that we’d like to find the y-value associated with a new x-value of **13**.

We can use the following code to do so:

**import scipy.interpolate
y_interp = scipy.interpolate.interp1d(x, y)
#find y-value associated with x-value of 13
print(y_interp(13))
33.5**

The estimated y-value turns out to be **33.5**.

If we add the point (13, 33.5) to our plot, it appears to match the function quite well:

import matplotlib.pyplot as plt #create plot of x vs. y plt.plot(x, y, '-ob') #add estimated y-value to plot plt.plot(13, 33.5, 'ro')

We can use this exact formula to perform linear interpolation for any new x-value.

**Additional Resources**

The following tutorials explain how to fix other common errors in Python: