1.2: Linear Functions

Main Points.
This chapter discussed linear functions. They are data representations that produce straight lines as their graphs because the differences between two y-values and their corresponding x-values remain the same. The rate of this comparative increase in their values (ratio) is called the slope (m) of a function and is calculated by dividing the differences in the y-values by that of the x-values. This value along with a vertical intercept (b) is used to create the general formular for linear functions: y = b + mx. The equation of the line could also be written in poin-slope form: y – y0 = m(x – x0). A linear function which can have different m and b values belongs to a family and each different function shares a similiar trait: a straight line as a graph.

Challenges
What happens when you do not have a starting point (a "b")? Would you have to simply randomly pick one? Such as with time...there is no sure start of time; but for certain purposes we have to simply pick a place to start. Does that not make the data somewhat inaccurate?
Also the families of linear functions is confusing...according to the section, linear functions are their own relatives.

Reflections
Its interesting to think that there is really nothing in real life that fits perfectly in a linear functions (at least none I can think of); well yes when the data is restricted, but when a larger amount is considered such as with the Olympic and World Records the slope is no longer constant and thus the graph is not a straight and the function not linear. Thus in essence...linear functions could possibly be entirely theoretical.