CHAPTER 8 - GRAPHS AND SYSTEMS OF LINEAR EQUATIONS

OBJECTIVES

• Identify the basic terminology of rectangular coordinate systems.
• Express linear equations in standard form and slope-intercept form.
• Determine the slope and y-intercept of a line from its equation.
• Graph a linear equation using the table of values, slope-intercept, and x- and y-intercepts.
• Determine the equation of a line from a graph.
• Determine the equations of parallel and perpendicular lines.
• Classify systems of linear equations.
• Solve linear systems graphically and using the substitution and elimination methods.
• Write and solve systems of equations to word problems.

CHAPTER OUTLINE

8.1 Rectangular Coordinate System

8.2 Graphing Linear Equations

8 Review Exercises

8 Self-Test Exercises

Introduction

A linear equation describes a relationship in which the value of one variable depends on the value of another. The solutions to a linear equation are ordered pairs of numbers in which each number replaces one of the variables in the equation. An illustrative way to depict a linear equation with two variables is a straight line graph on a two dimensional coordinate axis system.

A 'system' of linear equations is a set of equations considered together. The simplest system of linear equations is one with two equations, each with the same two variables. These systems can be solved by several methods, including a graphical approach (by plotting the equations on the same graph) and algebraic approaches (such as the substitution and elimination methods). Many word problems in life can be solved by translating them into systems of linear equations.

In this chapter, we will learn to graph individual linear equations, and to solve systems of linear equations with two variables, both graphically and algebraically.