Beginning Algebra, 11th Edition

Graphing a Linear Equation

Graph

At least two different points are needed to draw the graph. First let and

then let in the equation to complete two ordered pairs.

Let. Let Multiply. Multiply. Subtract. Subtract.

y =- 4 Divide by. x = 5 Divide by 4.

- 5 y= 20 4 x= 20

0 - 5 y= 20 4 x- 0 = 20

4102 - 5 y= 20 x= 0 4 x- 5102 = 20 y=0.

4 x- 5 y= 20 4 x- 5 y= 20

y= 0

x= 0

4 x- 5 y=20.

EXAMPLE 1

Notice that the points plotted in FIGURE 7all appear to lie on a straight line, as

shown in FIGURE 8. In fact, the following is true.

Every point on the line represents a solution of the equation

and every solution of the equation corresponds to a point on the line.

The line gives a “picture” of all the solutions of the equation The line

extends indefinitely in both directions, as suggested by the arrowhead on each end.

The line is called the graphof the equation, and the process of plotting the ordered

pairs and drawing the line through the corresponding points is called graphing.

x+ 2 y=7.

x 2 y7,

188 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

OBJECTIVES OBJECTIVE 1 Graph linear equations by plotting ordered pairs. We know

that infinitely many ordered pairs satisfy a linear equation in two variables. We find

these ordered-pair solutions by choosing as many values of x(or y) as we wish and

then completing each ordered pair. For example, consider the equation

If we choose then so the ordered pair is a solution.

is a solution.

This ordered pair and other solutions of x+ 2 y= 7 are graphed in FIGURE 7.

1 + 2132 = 7 (1, 3 )

x= 1, y=3, 1 1, 3 2

x+ 2 y= 7.

Graphing Linear Equations in Two Variables

3.2

1 Graph linear equations by plotting ordered pairs. 2 Find intercepts. 3 Graph linear equations of the form. 4 Graph linear equations of the form or. 5 Use a linear equation to model data.

y=k x=k

Ax+By= 0

-5-4-3 -2 -1 1 2 3 4567

1 0

2

3

4

5

x

y

(1, 3) (3, 2) (7, 0)

(–2, )^92

(–3, 5) (–1, 4) (6, )^12

(0, )^72

FIGURE 7