# Lesson 8

Comparing Relationships with Equations

### Lesson Narrative

This lesson continues the work students did in the previous lesson on comparing proportional and nonproportional relationships. The focus is on students seeing the connection between the form of the equation and the kind of relationship it represents (MP7). Students should see by the end of this lesson that equations of the form $$y = kx$$ characterize proportional relationships.

### Learning Goals

Teacher Facing

• Compare and contrast (orally) equations that do and do not represent proportional relationships.
• Generalize that an equation equivalent to the form $y=kx$ can represent a proportional relationship.
• Use a table to determine whether a given equation represents a proportional relationship, and justify (in writing) the decision.

### Student Facing

Let’s develop methods for deciding if a relationship is proportional.

### Required Preparation

Calculators can optionally be made available to take the focus off computation.

### Student Facing

• I can decide if a relationship represented by an equation is proportional or not.

Building On