Algebra 1 · Chapter 3 of 8

Linear Functions and Graphs

Connect equations, tables, graphs, slope, and intercepts so a line becomes a meaningful rate-and-starting-value model.

Why this chapter matters

Linear functions are the first major function family and a foundation for comparing rates, reading trends, and choosing useful models.

What you will learn

  • Calculate and interpret slope as a rate of change.
  • Graph a line from an equation, table, or two points.
  • Write equations in slope-intercept and point-slope forms.

Lessons in this chapter

  1. Graphing linear functionsPlot lines from equations and tables. Read the full guide →
  2. Slope and rate of changeCalculate rise over run and interpret units.
  3. Slope-intercept formUse y = mx + b to identify rate and starting value. Read the full guide →
  4. Writing a line from dataBuild a linear equation from points or a real situation.

Study task

Compare two taxi plans by writing and graphing each fare equation. Identify where the plans cost the same.

Chapter checkpoint

What are the slope and y-intercept of y = -3x + 5?

The slope is -3 and the y-intercept is 5, so the line passes through (0, 5).