Where do those linear functions in the book come from?  We use pairs of data points to form ordered pairs, and we graph those ordered pairs.  If it is apparent that a line would approximate the ordered pairs, we find the equation of that line by choosing the appropriate y-intercept and slope.  Graphing calculators will compute this linear equation for us by the method known as linear regression, a topic normally reserved for statistics courses. 

Consider the following table of data. 
 

Enter the data points (see first graph).  Graph the data points as a scatterplot (second graph).  Create the linear regression line that approximates the data points and graph the line (third graph). 

Given the linear regression equation y = 1.45x + 56, you can predict future test grades based on the amount of study time you spend in this class. 

 

Graphing Calculator Explorations
Redevelop the example above on your calculator.  How many hours must you spend in order to get an A (90% or higher) on the next test? Use regression analysis to find the linear equation that models the data below:   5.1 3.4 5.6 8.1 9.4 4.1 6.4 3.8 1.2 0.8   What is the y-value, given that x = 4.8?