Beginning Algebra, 11th Edition

Writing an Equation of a Line

Write an equation of the line with slope and y-intercept

Here, and so the equation is

Slope y-intercept is

Slope-intercept form

y= NOW TRY

2

3

x+ 1 - 12 , or y=

2

3

x-1.

y= mx+ b

1 0, b 2.

m= b=-1,

2

3

1 0, - 12.

2

3

EXAMPLE 2

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

OBJECTIVE 2 Graph a line by using its slope and a point on the line. We

can use the slope and y-intercept to graph a line.

Given the slope and y-intercept of a line, we can write an equation of the line.

Graphing Lines by Using Slopes and y-intercepts

Graph the equation of each line by using the slope and y-intercept.

(a)

Step 1 The equation is in slope-intercept form.

Slope Value of bin y-intercept

Step 2 The y-intercept is Graph this

point. See FIGURE 30.

Step 3 The slope is By the definition of

slope,

From the y-intercept, count up 2 units

and to the right 3 units to obtain the

point

Step 4 Draw the line through the points

and to obtain the graph

in FIGURE 30.

1 0, - 12 1 3, 1 2

1 3, 1 2.

m=

change in y (rise)

change in x (run)

=

2

3

.

2

3.

1 0, - 12.

1 0, b 2

y=

2

3

x- 1

y=

2

3

x- 1

EXAMPLE 3

NOW TRY
EXERCISE 2
Write an equation of the line
with slope and y-intercept
1 0, 2 2.

- 4

NOW TRY ANSWER
2.y=- 4 x+ 2

Graphing a Line by Using the Slope and y-Intercept

Step 1 Write the equation in slope-intercept form, if necessary, by solving

for y.

Step 2 Identify the y-intercept. Graph the point.

Step 3 Identify slope m of the line. Use the geometric interpretation of

slope (“rise over run”) to find another point on the graph by count-

ing from the y-intercept.

Step 4 Join the two points with a line to obtain the graph. (If desired,

obtain a third point, such as the x-intercept, as a check.)

1 0, b 2

x

y

(0, –1)

Up 2

Right 3

y-intercept

(3, 1)

m =^23

y = 32 x – 1

FIGURE 30

http://www.ebook777.com

http://www.ebook777.com