# Chapter 9: Linear Functions and Graphs

## Introduction

Here you will explore linear functions and graphs. You will begin with functions. You will learn how to identify, describe and write functions. This will involve function rules, function notation and function tables. Next, you will learn about slope and about how to use intercepts. Then, you will explore linear equations and slope together and will learn new ways to write linear equations. Next, you will recognize, solve and graph linear systems of equations. Finally, you will solve and graph linear inequalities.

## Chapter Outline

- 9.1. Recognizing Functions
- 9.2. Evaluating Function Rules
- 9.3. Writing Function Rules
- 9.4. Finding Solutions for Equations in Two Variables
- 9.5. Using Tables to Graph Functions
- 9.6. Using Intercepts
- 9.7. Finding the Slope of a Line
- 9.8. Direct and Inverse Variation
- 9.9. Using Slope-Intercept Form
- 9.10. Graphing Linear Equations
- 9.11. Writing Linear Equations
- 9.12. Use Function Notation to Graph Functions
- 9.13. Recognizing Linear Systems
- 9.14. Solving Linear Systems by Graphing
- 9.15. Solving Linear Systems by Substitution
- 9.16. Solving Linear Inequalities
- 9.17. Graphing Linear Inequalities

### Chapter Summary

## Summary

First, you learned all about functions. You learned how to identify functions, how to evaluate function rules and how to use input/output tables. You learned how to find solutions for equations in two variables, and you learned how to graph functions.

Then you learned about slope. You learned to identify the slope in an equation as well as on a graph. You learned how to write equations in different forms including standard form and slope-intercept form. You saw how to identify the slope and the y-intercept in both an equation and on a graph.

Finally, you learned about linear systems of equations and inequalities. With systems of linear equations, you learned how to identify them and to solve them through substitution and through graphing. Then you learned how to solve linear inequalities and how to graph them on the coordinate plane.