Discovery Lesson Writing Equations (Perpendicular)

Discovery LessonDiscovery LessonDiscovery LessonDiscovery LessonWriting EquationsWriting Equations(Perpendicular)(Perpendicular)

) 2 3) 2 8 B xA y yx x x

2 8 y x 2 2 2

14

2y x

2x 2x

2 3 y x

What do you notice about the two equations?

• Signs of the Slopes? ___________ • Numbers that make the Slopes?___• How are they related to each other?

___________________________• What would happen if I multiplied the

slopes together?

• What does that mean?___________

1) 4

2A y x ) 2 3 B y x

1

2 2

1

2

2

1 Negative reciprocals of each other

Predict what you think the graphs will look like based on what you know about slope

and y-intercepts

• Increasing?•Decreasing?•Do they Cross?

1) 4

2A y x ) 2 3 B y x

) 2 3 B y x

1) 4

2A y x

What does What does this this

Square tell Square tell you?you?

What are the properties of a square?

Were you correct in your prediction?

14

2y x 2 3 y x

1) 1

3C y x

) 3 2D y x

What does What does this this

Square tell Square tell you?you?

1) 1

3C y x

) 3 2D y x

What happens when What happens when you multiply the you multiply the slopes together?slopes together?

1 3 1

1

33

3

1) 1

3C y x ) 3 2D y x

What is the cause of this special relationship?

_________________________________________

Explain how you can look at two equations in slope-intercept form to determine if they have this special relationship. ______________________________________________________

Compare the pairs below:

4 5) 1 ) 8

5 4E y x F y x

1 1) 2 ) 2

3 3G y x H y x

) 4 5 ) 4 6I y x J y x 1

4

If I gave you an equation, can you write another equation so the two lines would be perpendicular to each other.

21) 5

3y x

12) 6

4y x

3) 5 4y x

now go to next column

3) Find line perpendicular to and goes through (-3, 4)

1 1( , )x y

2 ( 3)4 b4 6 b

66b2

__ __y x

2 2y x

2 2

22

1m

Step 1 Step 2 Step 3

15

2y x

1

2y = x 5

FLIP the slope &

CHANGE the SIGN

now go to next column

3) Find line perpendicular to and goes through (-3, 4)

1 1( , )x y

2 ( 6)4 b4 12 b

1212b8

__ __y x

2 2y x

2 8

22

1m

Step 1 Step 2 Step 3

15

2y x

1

2y = x 5

FLIP the slope &

CHANGE the SIGN

Perpendicular Lines (symbol) • Lines that form a 90° Angle.• Perpendicular Lines have one solution

written as an ordered pair.• Perpendicular Lines’ slopes are NOT the

same (negative reciprocals). • Do 2 things…

• FLIP the slope & • CHANGE the SIGN

m

3

2m

23

Given slope: Perpendicular slope:

5)

6mA

6

5m

1)

3B m

3

1m

3

4)

7C m 7

4

m

) 9D m 1

9m

now go to next column

3) Find line perpendicular to and goes through (-6, 4)

1 1( , )x y

3 ( 6)4 b4 18 b

1818b14

__ __y x

3 14y x

3 14

33

1m

Step 1 Step 2 Step 3

14

3y x

1

3y = x+4

FLIP the slope &

CHANGE the SIGN

now go to next column

4) Find line perpendicular to and goes through (4, 7)

1 1( , )x y

y bmx 2

5

(4)7 b

7 8

5 b

88

b27

5

y bmx

__ __y x

2 27

5 5y x

2

5

27

5

2

5m

Step 1 Step 2 Step 3

5 2 10x y

5 2 10x y

5x 5x2 5 10y x

55

2y x

2 2 2(5) (5) (5)

35 8 5b

5b275 5

FLIP the slope &

CHANGE the SIGN