Intermediate Algebra (11th edition)

Use either or as in the point-slope form of the equation of a

line. We choose so and

Point-slope form

Definition of subtraction

Multiply by 9 to clear the fraction.

Standard

Distributive property

form Add 10x. Add 27.

Verify that if were used, the same equation would result. NOW TRY

OBJECTIVE 6 Write an equation of a line parallel or perpendicular to a

given line.As mentioned in Section 3.2,parallel lines have the same slope and per-

pendicular lines have slopes that are negative reciprocals of each other.

Writing Equations of Parallel or Perpendicular Lines

Write an equation of the line passing through the point and (a)parallel to the

line (b)perpendicular to the line Give final answers in

slope-intercept form.

(a)We find the slope of the line by solving for y.

Subtract 2x.

Divide by 3.

Slope

The slope of the line is given by the coefficient of x,

so See FIGURE 30.

The required equation of the line through and parallel to

must also have slope To find this equation, we use the point-slope form, with

and

Definition of subtraction

Distributive property

Add 6.

We did not clear the fraction here because we want

the equation in slope-intercept form—that is, solved

for y. Both lines are shown in FIGURE 31.

y=-

2

3

x+ 4

y- 6 =-

2

3

x- 2

y- 6 =-

2

3

1 x+ 32

y - 6 =- y 1 =6,m=- 32 ,x 1 =- 3

2

3

3 x- 1 - 324

1 x 1 , y 12 = 1 - 3, 6 2 m=- 32.

- 23.

1 - 3, 6 2 2 x+ 3 y= 6

m=- 23.

y= -

2

3

x+ 2

3 y=- 2 x+ 6

2 x+ 3 y= 6

2 x+ 3 y= 6

2 x+ 3 y=6; 2 x+ 3 y=6.

1 - 3, 6 2

EXAMPLE 6

1 5, - 72

10 x+ 9 y=- 13

9 y- 27 =- 10 x- 40

9 y- 27 =- 101 x+ 42

y- 3 =-

10

9

1 x+ 42

y - 3 = - y 1 =3,m=- 109 ,x 1 =- 4

10

9

3 x- 1 - 424

y- y 1 = m 1 x- x 12

1 - 4, 3 2 , - 4 =x 1 3 = y 1.

1 - 4, 3 2 1 5, - 72 1 x 1 , y 12

SECTION 3.3 Linear Equations in Two Variables 165

2 x + 3 y = 6 m^ = –^23

y

x

–4 0

2

5

3

FIGURE 30

y

–3 0

2

4

36

(–3, 6)

x

y = –^23 x + 4

y = –^23 x + 2

6

FIGURE 31

NOW TRY
EXERCISE 5
Write an equation of the line
passing through the points
and.
Give the final answer in
standard form.

1 3, - 42 1 - 2, - 12

NOW TRY ANSWER

5. 3 x+ 5 y=- 11