composing lines on top of lines and you're going to get another line right so this is the best you'll be able to do with the linear activation function on the other hand nonlinearities allow you to approximate arbitrarily complex functions by kind of introducing these nonlinearities into your decision boundary and this is what makes neural networks extremely powerful let's understand this with a simple example and let's go back to this picture that we had before imagine I give you a train network with weights W on the top right so W here is 3 and minus 2 and the