discovery lesson writing equations (perpendicular)
TRANSCRIPT
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