A lot of information is covered in this section, and it may take a while for the students to finish the spreadsheet activity, depending on their proficiency with Excel. I felt that for the students to really learn about linear functions, they may need more that 50 minutes.
Objectives:
To recognize linear functions.
To find an equation of a linear function given certain information
Materials:
Microsoft Excel
Graphing Calculator with overhead
Graph paper
Procedure:
Begin the lesson with reviewing some of the data sets from the day before. Let's take height versus arm span. Collect the data from each student (tell them to convert to inches or centimeters only). Have the students put this data into an Excel spreadsheet (ordered from shortest to tallest). Click here for a short example. Let them graph the information using Excel. It should be linear (or almost linear). This is just an example of how a linear function is important in real life.
Discuss and define a linear function.
Discuss slope and y-intercept.
Find an equation of a linear function for which f(2)=5 and f(6)=3.
Do several other examples of this nature.
Graph f(x) = x on the overhead.
Graph f(x) = x + 2
Graph f(x) = x - 2
Discuss how this shifts the graph of f(x) = x.
Graph f(x) = 2x on the overhead.
Graph f(x) = (1/2)x and discuss how the slope affects a linear function.
Have the students sketch several linear functions on graph paper.
Discuss the vertical line.
Have the students find a linear equation that best approximates various data sets, including height versus arm span. Discuss positive and negative correlations.
Classwork/Homework: pg. 629-631 #1-31 odd, 39-42.