The purpose of this lesson is for students to understand that while there are many ways to scale axes when graphing a proportional relationship, certain ranges for the axes are helpful for seeing specific information.

Students begin by considering a claim that the graph of one line is steeper than the graph of a second line. While one graph looks like a steeper line, by noticing the scale of the axes of each graph, it can be determined that the two lines actually have the same slope. Next, students sort graphs on cards based on what proportional relationship they represent (MP7). Each graph has a different scale, with some scales purposefully quite different, pressing the need to pay attention to scale and rely on mathematical definitions of steepness, not just visual ones.

Then students graph a proportional relationship on two differently scaled axes, comparing it to the graph of a nonproportional relationship. By looking at the same two relationships graphed at different scales, students see how the scale of the axes affects the information that can be determined.