Alg1 Lesson 1.17 Special Slopes

Lesson 1.17: Special Slopes

Obj: 2E, 2F, 2G: I can formulate linear equations with
special slopes.

EQ: How can I determine if a slope is parallel,
perpendicular, zero, or undefined?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

What role will you be today?

• Facilitator

• Scribe

• Resourcer

• Includer

• All of them (I will be by myself)

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

When waiting for other groups to be ready…

Part 1: Parallel Lines

Steps:

●Solve for y

●Check the slopes

Parallel lines have no solution to systems of equations!

Graph Examples: Find Slope of 2 Points

Parallel

Not Parallel

Equation Examples: Solve for y, compare slopes

Parallel

y = 3x + 2 and y = 3x - 7

2x + 6y = 12 and 3x + 9y = 27

6y = -2x + 12 9y = -3x + 27

y = -(2/6)x + 12/6 y = -(3/9)y + 27/9

y = -⅓x + 2 y = -⅓x + 3

Not Parallel

y = 3x + 2 and y = -3x - 7

2x + 6y = 12 and 3x - 9y = 27

6y = -2x + 12 -9y = -3x + 27

y = -(2/6)x + 12/6 y = (-3/-9)x + 27/-9

y = -⅓x + 2 y = ⅓x - 3

Categorize

Options (6)

y = (6/8)x + 1 and y = (3/4)x + 2

y = 3x + 1 and y = -3x + 2

6x + 10y = 30 and 3x + 5y = 60

2x + 5y = 10 and 2x - 5y = 10

Categorize each as Parallel or Not Parallel.

Parallel

Not Parallel

Word Cloud

Write your favorite equipment on a playground.

Part 2: Perpendicular Lines

Steps:

●Solve for y

●Check the slopes

●The product of slopes is -1

Perpendicular lines form a 90 degree angle.

Graph Examples: Find Slope of 2 Points

Perpendicular

Not Perpendicular

Equation Examples: Solve for y, compare slopes

Perpendicular

y = 2x + 7 and y = -½x + 3

(2)(-½) = -1

3x + 4y = 12 and 4x - 3y = 24

4y = -3x + 12 -3y = -4x + 24

y = -(¾)x + 12/4 y = (-4/-3)x + 24/-3

y = -¾x + 3 y = (4/3)x - 8

(-¾)(4/3) = -1

Not Perpendicular

y = 2x + 7 and y = ½x + 3

(2)(½) ≠ -1

3x + 4y = 12 and 4x + 3y = 24

4y = -3x + 12 3y = -4x + 24

y = -(¾)x + 12/4 y = (-4/3)x + 24/3

y = -¾x + 3 y = (-4/3)x + 8

(-¾)(-4/3) ≠ -1

Categorize

Options (6)

y = ¼x + 1 and y = -4x + 2

y = 2x + 3 and y = -2x + 7

2x + 8y = 20 and 8x - 2y = 40

2x + 5y = 10 and 2x - 5y = 10

Categorize each as Perpendicular or Not Perpendicular

Perpendicular

Not Perpendicular

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Part 3: Horizontal & Vertical

Lines

y = -4

y = 0

y = -3

x = 3

x = -2

x = -3

Practice

Labelling

Fill in each blank.

Drag labels to their correct position on the image

Vertical

Horizontal

x = -1

y = 3

undefined

zero

Labelling

Fill in each blank.

Drag labels to their correct position on the image

Horizontal

zero

undefined

y = 5

Vertical

x = -4

Labelling

Fill in each blank.

Drag labels to their correct position on the image

y = -5

zero

undefined

Horizontal

Vertical

x = 1

Labelling

Fill in each blank.

Drag labels to their correct position on the image

zero

Vertical

Horizontal

undefined

x = 4

y = 4

Labelling

Fill in each blank.

Drag labels to their correct position on the image

Vertical

x = -5

y = -1

zero

undefined

Horizontal

Make 4 Quadrants, write down
properties for each type of line

Open Ended

Upload a pic of your notes here.