Identifying Proportional and Non-Proportional Relationships

The third page provides practical examples to distinguish between proportional and non-proportional relationships through graphical analysis.

Example: Three different graphs are shown:

1. Non-proportional: Points not aligned
2. Non-proportional: Points aligned but not passing through origin
3. Proportional: Points aligned and passing through origin

Highlight: The key to identifying proportionality in graphs is checking both alignment of points and passage through the origin.

Vocabulary:

• Proportional relationship: A relationship where quantities vary in a constant ratio
• Origin: The point (0,0) on a coordinate plane
• Aligned points: Points that form a straight line

Understanding Proportional Tables

The first page introduces the fundamental concept of reconnaître tableau de proportionnalité mathématiques. A proportional table is characterized by the ability to move from one row to another by multiplying or dividing by the same number, known as the coefficient of proportionality.

Definition: A proportional table is one where all quotients between corresponding values are equal, represented by the coefficient of proportionality.

Example: In a proportional table, if we have values (1,2,3,4,5) in one row and (3,6,9,12,15) in another, the coefficient of proportionality is 3, as each value in the second row is three times its corresponding value in the first row.

Highlight: To verify if a table represents a proportional relationship, all quotients between corresponding values must be equal.