Beginning Algebra, 11th Edition

(b)

Step 1 Solve for yto write the equation in slope-intercept form.

Subtract 3x.

Slope-intercept form Divide by 4.

Step 2 The y-intercept is Graph this

point. See FIGURE 31.

Step 3 The slope is which can be written

as either or We use here.

From the y-intercept, count down3 units

(because of the negative sign) and to the

right 4 units, to obtain the point

Step 4 Draw the line through the two points

and to obtain the graph in

FIGURE 31.

1 0, 2 2 1 4, - 12

1 4, -1).

m=

change in y (rise)

change in x (run)

=

- 3

4

• 3
  4

3

- 4.

• 3
  4

- 34 ,

1 0, 2 2.

y=-

3

4

x+ 2

4 y=- 3 x+ 8

3 x+ 4 y= 8

3 x+ 4 y= 8

SECTION 3.4 Writing and Graphing Equations of Lines 213

NOW TRY

NOTEIn Step 3 of Example 3(b),we could use for the slope. From the y-intercept,

count up 3 units and to the left4 units (because of the negative sign) to obtain the point

1 - 4, 5 2 .Confirm that this produces the same line.

3

• 4

NOTE In Example 4,we could have written the slope as instead. Verify that this

produces the same line.

4

• 1

OBJECTIVE 3 Write an equation of a line by using its slope and any point

on the line. We can use the slope-intercept form to write the equation of a line if

we know the slope and any point on the line.

NOW TRY ANSWERS
3.

4. 
   

(0, 2)

y

(4, –1)

Down 3

Right 4

y-intercept

m = – or^34 –3 4

3 x + 4y = 8

x

FIGURE 31

Isolate yon

one side.

Graphing a Line by Using the Slope and a Point

Graph the line through with slope

First, locate the point Write the slope as

Locate another point on the line by counting down

4 units and then to the right 1 unit. Finally, draw the

line through this new point Pand the given point

See FIGURE 32.

NOW TRY

1 - 2, 3 2.

m=

change in y (rise)

change in x (run)

=- 4 =

- 4

1

.

1 - 2, 3 2.

1 - 2, 3 2 - 4.

EXAMPLE 4

x

y

0

(2, 1)

(0, 4)

3 x + 2y = 8

NOW TRY
EXERCISE 4
Graph the line through
1 - 3, - 42 with slope^52.

x

y

0

(–3, – 4)

x

y

Right 1

Down 4

(–2, 3)

P

m = –4 1

FIGURE 32

NOW TRY
EXERCISE 3
Graph by using
the slope and y-intercept.

3 x+ 2 y= 8