4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper

4-7B Perpendicular Lines

Algebra 1 Glencoe McGraw-Hill Linda Stamper

What is the reciprocal of 8?What is the opposite reciprocal of 8?

In this lesson you will need to find and use opposite reciprocals.

81

81

Two lines in a coordinate plane are perpendicular if they intersect at right angles (90 degree angles).

Horizontal and vertical lines are perpendicular to each other.

x

y

In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is –1.

x

y

Do you think these lines are perpendicular?

How to determine whether lines are perpendicular.

1. Write each line in slope-intercept form.

2. Multiply the slopes together.

3. If the product is –1, then the lines are perpendicular.

Write the equation of each line in the graph. Determine whether the lines are perpendicular.

x

y

Green line

y-intercept is 3

bmxy

3x23

y

Blue liney-intercept is –

1

32

slope

bmxy

1x32

y

1x32

y 1

32

23

The lines are perpendicular!

23

slope

•

• ••

These are

opposite reciproca

ls!

Example 1 Write the equation of each line in the graph. Determine whether the lines are perpendicular.

x

y

Green liney-intercept is

3

bmxy 3xy

Blue liney-intercept is –

443

slope

bmxy

4x43

y

4x43

y

143

1

The lines are not perpendicular!

1 slope••

•

•

Example 2 Write the equation of each line in the graph. Determine whether the lines are perpendicular.

x

y

Green liney-intercept is

1

bmxy

1x23

y

Blue liney-intercept is –

432

slope

bmxy

4x32

y

4x32

y 1

32

23

The lines are perpendicular!

23

slope •

•

••

Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2.

x

y

(-4,-3)

•

••

bmxy

b441

3

b441

3

Find the slope of the given line. 4m

Find the opposite reciprocal.

41

m

Use slope-intercept or point-slope to write the equation.

b13 11

b2

2x41

y

•

2yx4

Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2.

Find the slope of the given line. 4m

Find the opposite reciprocal. 4

1

Use slope-intercept or point-slope to write the equation.

bmxy

b441

3

b13 11

b2

2x41

y

11 xxmyy

4x41

3y

3 3

4x41

3y

1x41

3y

2x41

y

2yx4 x4 x4

2x4y

(when no graph is given)

Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12.

Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3.

Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3.

Find slope of given line.

Find the opposite reciprocal.

Use slope-intercept or point-slope form to write the equation.

Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12.

Find slope of given line. 4

1m

Find the opposite reciprocal. 4

Use slope-intercept or point-slope form to write the equation.bmxy

b342

b122 1212

b1010x4y

11 xxmyy

3x42y

2 2

3x42y

12x42y

10x4y

12y4x x x

12xy4 4 4 4

3x41

y

Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3.

Find slope of given line. 3

2m

Find the opposite reciprocal.

2

3

Use slope-intercept or point-slope form to write the equation.bmxy

b423

7

11 xxmyy

4x23

7y

7 7

4x23

7y

6x23

7y

13x23

y

3y3x2 x2 x2

3x2y3 3 3 3

1x32

y b67

66b13

13x23

y

Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3.

Find slope of given line. 2

7m

Find the opposite reciprocal. 7

2

Use slope-intercept or point-slope form to write the equation.bmxy

b472

1

11 xxmyy

4x72

1y

1 77

4x72

1y

78

x72

1y

71

x72

y

3y2x7 x7 x7

3x7y2 2 2 2

23

x27

y b

78

78

78

b71

71

x72

y

177

Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.

What is the problem

asking you to do?x

y

•

-3x+2y=6

Write equation for

this line.

(but no graph is given)

Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.

Find slope of given line. 2

3m

Find the opposite reciprocal.

32

Find the x-intercept of the given line. 6y2x3

602x3 6y2x3

x3 x36x3y2

2 2 2

3x23

y 336x3

2x

Use slope-intercept or point-slope form to write the equation.

Coordinate of x-intercept is (-2,0).

bmxy

b232

0

b34

0

34

34

b34

34

x32

y

Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line.

x

y

•

34

x32

y

Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line.

Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line.

Find slope of given line.

Find the opposite reciprocal.

Use slope-intercept or point-slope form to write the equation.

Find the intercept of given line.

Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line.

Find slope of given line. 3

1m

Find the opposite reciprocal.

3

Find the x-intercept of the given line. 6y3x

603x 6y3x

x x6xy3

3 3 3

2x31

y

6x

Use slope-intercept or point-slope form to write the equation.

Coordinate of x-intercept is (6,0).

bmxy

b630

b180 1818b18

18x3y

Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line.

Find slope of given line. 2

3m

Find the opposite reciprocal. 3

2

Find the x-intercept of the given line. 8y2x3

8y203 8y2x3

x3 x38x3y2

2 2 2

4x23

y 228y2

4y

Use slope-intercept or point-slope form to write the equation.

Coordinate of y-intercept is (0,4).

bmxy

b032

4

b4

4x32

y

4-A15 Pages 240-241 #18–25,28-30,36 and

Skills Practice Wkbk. Page 30 #13-24.Review nightly for trimester 1 exam.