Students explore the idea that not all straight lines are proportional by comparing a graph representing a stack of books with a graph representing a stack of cups. They recognize that all proportional relationships are represented as a straight line that passes through the origin.
Not all graphs of straight lines represent proportional relationships.
There are three ways to tell whether a relationship between two varying quantities is proportional:
- The graph of the relationship between the quantities is a straight line that passes through the point (0, 0).
- You can express one quantity in terms of the other using a formula of the form y = kx.
- The ratios between the varying quantities are constant.
Goals and Learning Objectives
- Understand when a graph of a straight line is and when it is not a proportional relationship.
- Recognize that a proportional relationship is shown on a graph as a straight line that passes through the origin (0, 0).
- Make a table of values to represent two quantities that vary.
- Graph a table of values representing two quantities that vary.
- Describe what each variable and number in a formula represents.