# Chapter 3, Exploration 3

Building on exploration 2, you will consider the dynamics of the linear system $$x_{n+1} = mx_n +b$$ for nonzero values of $$b$$. How do the values of $$m$$ and $$b$$ affect the fixed point and/or its stability. Sliders adjust $$m,b,$$ and the initial condition $$x_0$$.

Make sure the sidebar is closed so you can see the sequence graph on the left and the stairstep diagram on the right simultaneously. Is the stability affected by the initial condition?

m:

b:

Initial Condition: