Intermediate Algebra (11th edition)

NOTE Every linear equation (of a nonvertical line) has a unique(one and only one)

slope-intercept form. In Section 3.6,we study linear functions,which are defined

using slope-intercept form. Also, this is the form we use when graphing a line with a

graphing calculator.

OBJECTIVE 2 Graph a line, using its slope and y-intercept.We first saw

this approach in Example 5(a)of Section 3.2.

Graphing Lines Using Slope and y-Intercept

Graph each line, using the slope and y-intercept.

(a)

Here, and Plot the y-intercept

The slope 3 can be interpreted as

From move 3 units upand 1 unit to the

right,and plot a second point at Join the

two points with a straight line. See FIGURE 26.

(b)

Write the equation in slope-intercept form by solving for y.

Subtract 2x.

Divide by 3.

Slope y-intercept is

Plot the y-intercept The slope can be inter-

preted as either or Using begin at

and move 2 units downand 3 units to the rightto

locate the point The line through these two

points is the required graph. See FIGURE 27. (Verify

that the point obtained with as the slope is also on

this line.)

2

• 3

1 3, 1 2.

1 0, 3 2

• 2

3 ,

2

- 3.

• 2
  3

1 0, 3 2.

1 0, 3 2.

y= -

2

3

x+ 3

3 y=- 2 x+ 9

3 y+ 2 x= 9

3 y+ 2 x= 9

1 1, - 32.

1 0, - 62 ,

m=

rise

run

=

change in y

change in x

=

3

1

.

1 0, - 62.

m= 3 b= - 6.

y= 3 x- 6

EXAMPLE 2

162 CHAPTER 3 Graphs, Linear Equations, and Functions

NOW TRY
EXERCISE 2
Graph the line, using the
slope and y-intercept.

4 x+ 3 y= 6

x

y

0

(1, –3)

(0, – 6)

y = 3x – 6

FIGURE 26

x

y

0

(3, 1)

(0, 3)

3 y + 2x = 9

y = –^23 x + 3

FIGURE 27

OBJECTIVE 3 Write an equation of a line, given its slope and a point on

the line.Let mrepresent the slope of a line and represent a given point on

the line. Let represent any other point on the line. See FIGURE 28.

Slope formula

Multiply each side by

Rewrite.

This last equation is the point-slope formof the equation of

a line.

y- y 1 =m 1 x- x 12

m 1 x- x 12 =y- y 1 x-x 1.

m=

y-y 1

x-x 1

1 x, y 2

1 x 1 , y 12

x

y

0

Slope is m.

Any other

point (x, y)

Given point

(x 1 , y 1 )

FIGURE 28

NOW TRY ANSWER
2.

0

y

x

(3, –2)

(0, 2)

4 x + 3y = 6

y = –^43 x + 2

NOW TRY