- Rates of change express themselves as slope of a line, and as a coefficient of x in a linear equation.
- Y-intercepts express themselves as constants in linear equations.
This bundle presumes that students have some experience with the coordinate plane, and with plotting points on the coordinate plane. They have not mastered the relationship between any of the forms of a linear equation and the associated graph. They may not know the terms slope or y-intercept. They have worked with algebraic variables. They know quite a bit about proportionality in general and rates in particular.
1 What are important features of lines?
The bundle opens with Polygraph: Lines in order to focus students’ attention on important characteristics of lines—especially steepness and x- and y-intercepts. The ideas that surface in students’ games provide a foundation for the work that follows.
2 What words do we use to name important features of lines?
This activity follows up on Polygraph: Lines, using the discussions (and students' informal language) in Polygraph to develop academic vocabulary related to the graphs of linear functions.