Lesson objective: Build on knowledge of proportional relationships to find rate of change and initial value for linear functions in various representations.

This lesson helps to build fluency with calculating rate of change and identifying initial value of linear functions. Graphs, tables, symbolic equations, and verbal descriptions are used here to help students build their understanding of rate of change and initial value by interpreting them in various representations. This work develops students' understanding that rate of change for general linear functions is similar to unit rate for proportional relationships.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they identify linear functions in various representations as proportional or non-proportional, and utilize this classification in answering questions about the functions.

**Key vocabulary:**

- initial value
- linear
- non-proportional
- proportional
- rate of change
- slope
*y*-intercept