In this lesson students connect linear relationships to functions and understand that any linear function can be represented by . They use linear functions to model real-world situations (MP4).

Students compare linear functions represented in different ways. They interpret the slope of the line as the rate of change of the dependent variable with respect to the independent variable and the vertical intercept of the line as the initial value of the function. 

Then they are given data for an almost linear relationship and develop a linear model. They use their model to make predictions and discuss the reasonableness of the model. They also consider a situation that they can make a linear model for, but it isn’t very accurate. When given data isn’t perfectly linear, students have to determine if a linear model is reasonable and what types of restrictions the model might need.

An optional activity offers additional practice with a situation that seems linear at first glance but is not. This activity works best when each student has access to a device that can run the applet, which allows students to plot values accurately.