Chapter 3 Chapter 3 Lesson 6Lesson 6

Objective: Objective: To relate slope and perpendicular lines.

If two nonvertical lines are perpendicular, the If two nonvertical lines are perpendicular, the product of their slopes is -1.product of their slopes is -1.

2 4 6 8

2468

-2-2

-4

-4

-6

-6

Example 1:Example 1:Checking for Perpendicular LinesChecking for Perpendicular Lines

Lines l1 and l2 are neither vertical nor horizontal. Are they perpendicular? Explain.

(-2,3)

(6,-3)

(0,2)

(-3,-2)

Slope of l1 )2(633

43

86

Slope of l2 )3(0)2(2

34

Lines Lines ll11 and and ll22 are are perpendicular because perpendicular because

the product of their the product of their slopes is -1.slopes is -1.

(-2,3) (6,-3)xx11 y y11 x x22 y y22

(-3,-2) (0 ,2)xx11 y y11 x x22 y y22

34

43

1

Find the product of the Find the product of the slopes.slopes.

2 4 6 8

2468

-2-2

-4

-4

-6

-6

Example 2:Example 2:Checking for Perpendicular LinesChecking for Perpendicular Lines

Lines l1 and l2 are neither vertical nor horizontal. Are they perpendicular? Explain.

(0,5)

(3,-2)

(5,5)(-4,1)

Slope of l1 0352

37

Slope of l2 )4(515

9

4

Lines Lines ll11 and and ll22 are not are not perpendicular because the perpendicular because the

product of their slopes is not product of their slopes is not -1.-1.

(0,5) (3,-2)xx11 y y11 x x22 y y22

(-4,1) (5,5)xx11 y y11 x x22 y y22

94

37

12728

Find the product of the Find the product of the slopes.slopes.

Example 3:Example 3:Checking for Perpendicular LinesChecking for Perpendicular Lines

Line l1 contains M(0,8) and N(4,-6). Line l2 contains P(-2,9) and Q(5,7). Are they perpendicular? Explain.

Slope of l1 0486

27

414

Slope of l2 )2(597

7

2

Lines Lines ll11 and and ll22 are not are not perpendicular because the perpendicular because the

product of their slopes is not product of their slopes is not -1.-1.

(0,8) (4,-6)xx11 y y11 x x22 y y22

(-2,9) (5,7)xx11 y y11 x x22 y y22

72

27

11414

Find the product of the Find the product of the slopes.slopes.

Example 4:Example 4:Writing Equations for Perpendicular LinesWriting Equations for Perpendicular Lines

Write an equation for the line perpendicular to y=-3x-5 that contains (-3,7)).

SlopSlopee

Use point-slope form to write an equation for the new line.Use point-slope form to write an equation for the new line.y-y1=mm(x-x1)

y-7=((11//33))(x-(-3))Y-7=(1/3)(x+3)

xx11 yy11

Find the negative reciprocal for the slope.Find the negative reciprocal for the slope.Slope=(-3)Negative Reciprocal = (1/3)

Example 5:Example 5:Writing Equations for Perpendicular LinesWriting Equations for Perpendicular Lines

Write an equation for the line perpendicular to 5y-x=10 that contains (15,-4).

Use point-slope form to write an equation for the new line.Use point-slope form to write an equation for the new line.y-y1=mm(x-x1)

y-(-4)=(-5-5))(x-15)y+4=(-5)(x-15)

xx11 yy11 Find the negative Find the negative reciprocal for the slope.reciprocal for the slope.

Slope=(1/5)Negative Reciprocal = -5

Get 5y-x=10 in Get 5y-x=10 in slope-intercept form.slope-intercept form.

5y-x=105y=x+10y=(1/5)x+2

Example 6:Example 6:Writing Equations for Perpendicular Writing Equations for Perpendicular

LinesLinesWrite an equation for the line perpendicular to 5x+2y=1 that contains (10,0)

Use point-slope form to write an equation for the new line.Use point-slope form to write an equation for the new line.y-y1=mm(x-x1)

y-(0)=(22//55))(x-10)y=(2/5)(x-10)

xx11 yy11 Find the negative Find the negative reciprocal for the slope.reciprocal for the slope.

Slope=(-5/2)Negative Reciprocal =(2/5)

Get 5x+2y=1 in Get 5x+2y=1 in slope-intercept form.slope-intercept form.

5x+2y=12y=-5x+1y=(-5/2)x+(1/2)

Homework

pg.161-163 #16-30;35;38