Lesson 5.8 Slopes of Parallel & Perpendicular Lines

Lesson 5.8 Slopes of Parallel & Perpendicular Lines

Learning Goals:

• I can identify and graph parallel and perpendicular lines.

• I can write equations to describe lines parallel or perpendicular to a given line.

Vocab:

• Parallel Lines: 2 lines that never touch (intersect) --> They have the same ________________!

• Looks like:

Review: how to find slope!

Multiple Choice

Find the slope of:

(7,1) and (-2,1)

• 0

• -1/2

• undefined

• -8

Multiple Choice

Find the slope of:

(1,8) and (3,12)

• 2

• 1/2

• 9/7

• -2

Parallel slopes are?...

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

What slope is parallel to:  
m = 4

• 4
• -1/4
• -4
• 1/4

Multiple Choice

What slope is parallel to:  
m = 3/4

• 4/3
• 3/4
• -3/4
• -4/3

Example 1A:

Identify which lines are parallel:

 $y=\frac{4}{3}x+3$ 

  $y=2$  

 $y=\frac{4}{3}x-5$  

 $y=-3$  

Example 1B:

Identify which lines are parallel:

 $y=3x+2$ 

  $y=-\frac{1}{2}x+4$  

 $x+2y=-4$  

 $y-5=3\left(x-1\right)$  

End of Day 1

Lesson 5.8 Day 2

Parallel & Perpendicular Lines

First, let's review parallel lines

Multiple Choice

Find the slope of the line that goes through the points (-8,6) and (7,-3).

• 1/3
• -1/3
• -3/5
• -5/3

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

y = 5/7x +2

y = 5/7x - 30

Are these lines parallel?

• Yes

• No

Multiple Choice

Are these two lines parallel?

y = -1/3x - 5

y = 1/3x + 2

• Yes

• No

Vocab:

• Perpendicular Lines: 2 lines that intersect & form a right angle --> They have ___________________________ slopes!

• Looks like:

• note: the product of the slopes = -1

Multiple Choice

What is the slope of a line perpendicular to a line with slope ^-6/₅ ?

• ^-6/₅
• ^-5/6
• ⁵/₆
• ^-4/₃

Multiple Choice

What is the slope of a line perpendicular to 5?

• 5

• 1/5

• -1/5

• -5

Example 3:

Identify which lines are perpendicular:

 $x=-2$ 

  $y=1$  

 $y=-4x$  

 $y+2=\frac{1}{4}\left(x+1\right)$  

Multiple Choice

The following represents slopes of two lines. Which answer choice describes the two lines?

m = 7 and m = -7

• Parallel

• Perpendicular

• Neither

Multiple Choice

y = 3/2x + 2
y = 2/3x + 6
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

Line 1: $\left(-1,\ 2\right),\ \left(2,\ 3\right)$  
Line 2:  $\left(0,\ 0\right),\ \left(3,\ 1\right)$  
These two lines are ______________________

• Parallel

• Perendicular

• Neither

End of Day 2

If have time, continue on

Write an equation that is parallel to:

 $y=\frac{4}{5}x+6$  

Write an equation that is perpendicular to:

 $y=-6x-4$  

Example 5A:

Write an equation in slope-intercept form for the line that passes through (4,5) and is parallel to the line described by y = 5x + 10.

Example 5B:

Write an equation in slope-intercept form for the line that passes through (3,2) and is perpendicular to the line described by y = 3x - 1.

Multiple Choice

What is the equation of a line parallel to the following line that passes through the given point? 
y = -4x + 6      (2, -1)

• y = 1/4x + 6
• y = -4x + 7
• y = -4x + 2
• y = 1/4x -1 

Multiple Choice

What is the equation of a line that is perpendicular to this line and goes through the given point?
y = 3x + 2      (3, -4)

• y = 3x - 2
• y = -1/3x - 5
• y = 3x - 4
• y = -1/3x - 3

Multiple Choice

The following represents slopes of two lines. Which answer choice describes the two lines?
 $m=-\frac{1}{3}$  and  $m=-\frac{1}{3}$  .

• Parallel

• Perpendicular

• Neither

Multiple Choice

y = -2/3x + 2
y = 3/2x + 9
These lines are...

• Parallel
• Perpendicular
• Neither

Want more practice?

Multiple Choice

y = 6x + 2
y = -6x + 2
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

y = 5/7x +2
y = 5/7x - 30
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

What slope is perpendicular to:  
m = 3

• -3
• -1/3
• 1/3
• 3

Multiple Choice

What slope is perpendicular to:  
m = 5/8

• -5/8
• 5/8
• -8/5
• 8/5

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

Use the equations given to determine if the following lines are parallel, perpendicular, neither or both.

y=4x-2

y-3=-1/4(x-8)

• parallel

• perpendicular

• neither parallel nor perpendicular

• both parallel and perpendicular

Multiple Choice

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

• Parallel
• Perpendicular
• Neither