Ms. Coombs begins with a reminder of an earlier problem about a pie eating contest.  She discusses the meaning of the elements of a linear function. This discussion follows her working to interpret y=mx+b style equations with the students. 

In this clip Ms. Coombs continues the discussion by asking about constant rates.  She steers the discussion towards constant speed and the rates in the linear functions.

Ms. Coombs continues to focus on the earlier pie eating function.  In this clip, she moves to a graphical representation for the function. In order to tie back into covaritational thinking she reminds the students about the finger tool.  She generates points on the graph by covariationally scaling the rate.

In this clip Ms. Coombs works with the students to focus on the possible points between plotted points on the graph of the linear function.  She explains why the intermediate points exist and why those points lie on the line.  She focuses on how changes in x determine the changes in y, based on the rate of change.