Overview
This lecture covers key concepts about proportional relationships, including how to identify, compare, and represent them using tables, graphs, and equations, as well as how to solve problems involving proportions.
Constant of Proportionality
- The constant of proportionality (k) is the ratio between two proportional quantities.
- It can be found using graphs, equations, or tables by dividing one variable by another.
- In equations, proportional relationships are written as y = kx.
Comparing and Interpreting Constants
- Proportional relationships can be compared by looking at their constants of proportionality.
- The greater the constant, the steeper the graph representing the relationship.
- Interpretation of the constant explains how much one quantity changes relative to the other.
Identifying Proportional Relationships
- A relationship is proportional if the ratio between two quantities remains constant.
- In real-life word problems, check if doubling one quantity doubles the other.
- Proportional relationships can be represented with tables, equations, and graphs.
Graphs of Proportional Relationships
- Proportional relationships appear as straight lines through the origin on a graph.
- The slope of the line represents the constant of proportionality.
- Identifying these lines helps determine if a relationship is proportional.
Writing and Solving Proportions
- Proportion equations show two ratios are equal, allowing you to solve for unknowns.
- Cross-multiply to solve proportion equations.
- Writing proportions helps set up and solve real-world word problems.
Equations of Proportional Relationships
- Proportional relationships can be expressed as equations like y = kx.
- Tables of values can be used to derive the equation by finding the constant of proportionality.
- Equations make it easier to predict values for given inputs.
Key Terms & Definitions
- Proportional Relationship — A relationship where the ratio between two variables is constant.
- Constant of Proportionality (k) — The fixed ratio in a proportional relationship (y = kx).
- Proportion — An equation stating that two ratios are equal.
Action Items / Next Steps
- Practice identifying and representing proportional relationships using tables, graphs, and equations.
- Complete quizzes and unit test to check understanding.
- Review worked examples and solve word problems involving proportions.