Proportional and Non proportional Representation

The Basics of Proportionality (00:00 - 01:15)

• Introduction to the difference between proportional and non-proportional relationships using social metaphors.

• Definition of a proportional relationship as one that is consistent and passes through the origin $(0,0)$.

Proportional Characteristics and Formulas (01:15 - 02:30)

• Explanation of the formula $y = kx$.

• Introduction of the Constant of Proportionality ($k$) and how it represents a steady rate of change without any initial offsets.

Non-Proportional Relationships and Fees (02:30 - 03:20)

• Discussion of non-proportional relationships using the example of a gym membership with an initial fee.

• Explanation of the slope-intercept form $y = mx + b$, where the $b$ represents a non-zero starting value.

Identification and Ratios (03:20 - 04:00)

• Tips for identifying relationships in tables and graphs.

• Comparing the ratio of $y/x$ to determine if a relationship is consistent or affected by a starting constant.