Lesson 6

The previous lesson looked in depth at an example of a linear relationship that was not proportional and then examined an interpretation of the slope as the rate of change for a linear relationship. In this lesson, slope remains important. In addition, students learn the new term vertical intercept or \(y\)-intercept for the point where the graph of the linear relationship touches the \(y\)-axis. 

In the first activity, students match situations to graphs and then interpret different features of the graph (slope and \(y\)-intercept) in terms of the situation being modeled (MP2). In the second activity, students analyze a common error, studying what happens when the slope and \(y\)-intercept are interchanged. This provides an opportunity to see how the \(y\)-intercept and slope influence the shape and location of a line: the \(y\)-intercept indicates where the line meets the \(y\)-axis while the slope determines how steep the line is. 

Interpreting features of a graph or an equation in terms of a real-world context is an important component of mathematical modeling (MP4).

Print and cut up slips from the Slopes, Vertical Intercepts, and Graphs blackline master. Prepare 1 set of cards for every 2 students.