At the end of this lesson, students will be able to:
- Identify direct variation.
- Graph direct variation equations.
- Solve real-world problems using direct variation models.
Terms introduced in this lesson:
constant of proportionality
Teaching Strategies and Tips
Use Examples 1-3 to motivate direct variation.
- Direct variation is an expression of a simple linear relationship with y−intercept =0. Since the line passes through origin, (0,0) is a point on it.
- The slope of the line is the constant of proportionality and is the only parameter in the problem. Therefore, it takes only one more point to determine the line (to determine the constant of proportionality).
- Emphasize the switch from m (slope) to k (constant of proportionality) is only notational.
By solving applied problems involving direct variation, teachers demonstrate the usefulness of these models.