# Patterns and Relationships: Level 5

The key idea of patterns and relationships at level 5 is that graphs and equations which represent a relationship between variables connect with each other in key and consistent ways.

Linear relationships can be expressed in the equation form y = mx + c, where m is the gradient of the graph of the relationship, and c is the y-intercept. It is important for students to understand the connections between the graphs and equations of a relationship and the context to which it relates. For example, y could represent the total savings, m the consistent amount saved or spent every week, x the number of weeks of saving or spending, and c the amount in the savings account at the beginning. As an example, \$25 is spent every week, and the beginning amount is \$100:  At this level students start to explore quadratic equations which represent a non-linear relationship between two variables. Often this is introduced using a geometric model such as the area of squares:  This key idea develops from the key idea of patterns and relationships at level 4, focussed on generalising patterns and relationships and expressing them as algebraic equations.

This key idea is extended to the key idea of patterns and relationships at level 6 where the students explore the effects of transformations on functions.