Module 2 Overview: Linear Models and Systems

There are many things in life which change at a constant rate. For example, if you work and are paid $10.00 per hour, your compensation changes at a constant rate: for each additional hour you work, your pay increases by exactly $10.00. Thus, your pay (P) may be expressed as a linear function of the number of hours worked (h) as follows: P = 10h.

Yet there are other events and phenomena that do not exhibit a constant rate of change. For instance, if you observed the number of birds at a bird feeder in your backyard each hour for ten hours, how could you describe the results? Do you think there would be a constant change in the number of birds each hour? Probably not. But maybe you could determine a linear function, with a constant slope, that would best approximate the data, and then use that function to estimate the number of birds at the feeder during those hours you did not collect data.

In this Module, you will investigate the properties and applications of linear functions. First, you will learn how to determine the equation of a linear function, given specific data, and then graph that function to analyze its behavior. Thereafter, you will learn how to use linear functions to model or approximate the relationship of data and use such linear functions to make predictions.

We begin with a review of the concept that expresses a constant rate of change: slope.