Lesson 5: Introduction to Linear Functions

• What makes a function linear?
• Why do some points form a straight line?
• What does a constant rate of change mean?
• How do we recognize linear functions?

Linear, straight line, constant rate of change, slope (introductory)

CCSS.MATH.8.F.A.3, CCSS.MATH.8.EE.B.5

Description: Students explore functions whose graphs form straight lines. Using input/output tables and graphs, they observe that the change between consecutive outputs is constant. They compare linear and non-linear functions. Purpose: To introduce the important category of linear functions and the concept of constant rate of change. DOK Level: 2-3 (Application)

• Visual comparison: Show linear and non-linear graphs side-by-side
• For struggling learners: Focus on simple linear functions (y = x, y = x + 1)
• For advanced learners: Introduce the concept of slope as rate of change
• Kinesthetic: Plot points on a large grid; see if they form a line

• Observation: Can students identify linear vs. non-linear functions?

• Worksheet: Given tables, identify which represent linear functions

• Graphing task: Plot a linear function and verify it forms a line

• Comparison: Explain why one function is linear and another is not

• Linear and non-linear function examples

• Input/output tables for comparison

• Coordinate plane worksheets

• Graph paper

• Resource: Khan Academy "Linear Functions" (adapted)