Course Overview

Linear equations and inequalities provide powerful tools for describing relationships, solving problems, and making predictions. From calculating costs and analyzing motion to modeling scientific data and making financial decisions, linear mathematics is used throughout everyday life and many professional fields. In this course, students will deepen their algebraic reasoning skills by learning how to solve equations and inequalities, analyze functions, graph relationships, and apply mathematical models to real-world situations.

Unit 1: Solving Linear Equations

Develop fluency in solving increasingly sophisticated linear equations.

1.1 Review of Algebraic Equations

  • Variables and constants
  • One-step and multi-step equations
  • Verifying solutions

1.2 Equations with Variables on Both Sides

  • Collecting like terms
  • Balancing equations
  • Efficient solving strategies

1.3 Equations with Fractions and Decimals

  • Clearing fractions
  • Working with decimal coefficients
  • Avoiding common errors

1.4 Literal Equations and Formula Rearrangement

  • Solving formulas for different variables
  • Using inverse operations
  • Applications in science and geometry

1.5 Real-World Equation Modeling

  • Translating situations into equations
  • Multi-step word problems
  • Practical applications

Unit 2: Understanding and Solving Inequalities

Learn how inequalities represent ranges of solutions and real-world constraints.

2.1 Introduction to Inequalities

  • Inequality symbols
  • Comparing quantities
  • Number line representations

2.2 Solving One-Step Inequalities

  • Addition and subtraction inequalities
  • Multiplication and division inequalities
  • Graphing solutions

2.3 Solving Multi-Step Inequalities

  • Combining operations
  • Isolating variables
  • Checking solutions

2.4 Compound Inequalities

  • AND inequalities
  • OR inequalities
  • Solution sets

2.5 Applications of Inequalities

  • Budgets and spending limits
  • Resource constraints
  • Decision-making scenarios

Unit 3: Linear Relationships and Functions

Explore how algebra describes relationships between changing quantities.

3.1 Patterns and Linear Relationships

  • Constant rates of change
  • Input-output tables
  • Linear patterns

3.2 Functions and Function Notation

  • Inputs and outputs
  • Function machines
  • Evaluating functions

3.3 Writing Linear Equations

  • Variables and relationships
  • Creating algebraic rules
  • Mathematical modeling

3.4 Direct Variation

  • Proportional relationships
  • Constant of proportionality
  • Applications

3.5 Comparing Representations

  • Tables
  • Equations
  • Graphs
  • Verbal descriptions

Unit 4: Graphing Linear Equations

Connect algebraic relationships to visual representations.

4.1 Review of the Coordinate Plane

  • Ordered pairs
  • Quadrants
  • Plotting points

4.2 Graphing from Tables

  • Creating tables of values
  • Plotting points
  • Drawing linear graphs

4.3 Slope and Rate of Change

  • Positive, negative, zero, and undefined slope
  • Interpreting slope
  • Real-world meaning

4.4 Slope-Intercept Form

  • Understanding y = mx + b
  • Slope and intercepts
  • Efficient graphing methods

4.5 Graphing Real-World Relationships

  • Distance-time graphs
  • Cost models
  • Scientific applications

Unit 5: Applications of Linear Models

Apply equations, inequalities, and graphs to meaningful situations.

5.1 Modeling with Linear Equations

  • Real-world scenarios
  • Creating equations
  • Making predictions

5.2 Modeling with Inequalities

  • Maximum and minimum conditions
  • Feasible solution regions
  • Practical applications

5.3 Systems of Linear Equations (Introduction)

  • Intersections of lines
  • Graphical solutions
  • Real-world interpretations

5.4 Linear Modeling Projects

  • Collecting data
  • Building models
  • Testing predictions

5.5 Capstone Algebra Project

  • Comprehensive investigation
  • Equations, inequalities, and graphs
  • Communicating mathematical conclusions

Course Summary

By the end of this course, students will understand how linear equations, inequalities, functions, and graphs can be used to describe and analyze relationships between quantities. They will be able to solve complex equations, graph linear relationships, interpret rates of change, and apply algebraic models to real-world situations.

Students will learn to:

  • Solve multi-step linear equations confidently.
  • Rearrange formulas and solve for unknown variables.
  • Solve and graph linear inequalities.
  • Interpret solution sets and constraints.
  • Understand and use function notation.
  • Model relationships using equations, tables, and graphs.
  • Calculate and interpret slope as a rate of change.
  • Analyze real-world situations using linear models.
  • Communicate mathematical reasoning clearly and logically.

This course serves as the cornerstone of algebraic mathematics, providing the skills and conceptual understanding needed for advanced algebra, quadratic functions, systems of equations, statistics, trigonometry, and many applications in science, engineering, economics, and technology. By mastering linear relationships, students gain powerful tools for understanding how quantities change and interact in both mathematics and the real world.

Last modified: Friday, 5 June 2026, 1:14 AM