# Chapter 4: Graphs of Equations and Functions

**At Grade**Created by: CK-12

## Introduction

Given a table or a function rule, how can you represent the data visually in two dimensions? Learning how to graph equations is not just a skill you will use in algebra. It is one you will carry with you throughout your mathematics studies.

This chapter will focus on graphing linear equations. After learning how to graph lines from tables and functions, you’ll be introduced to a line’s intercepts. You’ll also use graphs to find the slope of a line and the rate of change of a linear function.

Conversions, like dollars to Euros, kilograms to pounds, and Fahrenheit to Celsius, can all be modeled using linear equations. This chapter focuses on these applications and many more.

## Chapter Outline

- 4.1. Points in the Coordinate Plane
- 4.2. Graphs in the Coordinate Plane
- 4.3. Graphs of Linear Equations
- 4.4. Horizontal and Vertical Line Graphs
- 4.5. Intercepts and the Cover-Up Method
- 4.6. Slope
- 4.7. Rates of Change
- 4.8. Graphs Using Slope-Intercept Form
- 4.9. Graphs of Linear Models of Direct Variation
- 4.10. Graphs of Linear Functions
- 4.11. Problem Solving with Linear Graphs

### Chapter Summary

## Summary

This chapter begins with points and graphs in the coordinate plane. It then builds on these concepts with graphs of linear equations, vertical lines, and horizontal lines. It then discusses the intercepts of a line—how to find them and how to use them to graph and equation. Next it defines slope and rate of change and discusses how to find the slope of a line/the rate of change of a function. As part of this topic, direct variation models will be introduced, with an emphasis on real-world applications. Function notation, the vertical line test, and arithmetic progression will also be covered. Finally, the chapter concludes with the problem-solving strategies Read a Graph and Make a Graph.