In this lesson students continue their work with interpreting graphs of proportional relationships. An important goal of the lesson is for students to start to interpret the steepness of the graph in terms of the context. They use distance-versus-time graphs to decide which person from a group is going the fastest. They also work with graphs where the scale is not specified on each axis, and realize that they can still use graphs to compare rates.
- Create and interpret graphs that show two different proportional relationships on the same axes.
- Generalize (orally and in writing) that when two different proportional relationships are graphed on the same axes, the steeper line has the greater constant of proportionality.
Let’s graph more than one relationship on the same grid.
Have available the information from the activity "Tyler's Walk" from the previous lesson.
- I can compare two, related proportional relationships based on their graphs.
- I know that the steeper graph of two proportional relationships has a larger constant of proportionality.
The coordinate plane is a system for telling where points are. For example. point \(R\) is located at \((3, 2)\) on the coordinate plane, because it is three units to the right and two units up.
The origin is the point \((0,0)\) in the coordinate plane. This is where the horizontal axis and the vertical axis cross.