How can you use an equation to make a prediction from a pattern?

Equation > pattern > prediction

What are some predections

Normally, one would have a certain pattern and they would make an equation to make the prediction for what values would come next in a sequence (or at some x value), but if one had an equation such as y=3x+4 (I am using examples because this was a very general question) they could see that when x is 0 y=4 and that the y value increases three units for every change in x value. since y=4 when x=0, 4 may be called the initial value as well as the y-intercept (in fact this is generally true for all mathematical models). This is where the pattern starts.