Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

Open Ended

Do Now: What is the slope and y-intercept of the following linear equation?

y = 3x + 2 ?

Open Ended

Using desmos: https://www.desmos.com/calculator

Type in y = 3x + 2

Next, type in a separate line

y = mx + b and add the sliders.

Make the b (y-intercept any value other than 2).

Now use the slider for m, adjust the slider until the slope of the line is the same as y = 3x + 2.

Despite having different y-intercepts, what can we say about the two lines?

Open Ended

Finish the sentence:

Parallel lines have the same ________________.

Open Ended

What does the word perpendicular mean?

Graph the following linear equations using desmos.

• y = 3x + 2

• y = (-1/3)x + 5

• Describe the relationship between the two lines.

Parallel lines have the same slope.

y = 3x + 2

y = 3x + 5

Perpendicular lines have slopes that are the negative reciprocal of each other. i.e. 4 and -1/4,

1/3 and -3 etc.

Multiple Choice

Parallel lines have __________ slopes

• Equal
• Opposite
• Reciprocal 
• Total

Multiple Choice

Which figure shows a set of perpendicular lines?

• Figure 1
• Figure 2
• Figure 3
• Figure 4

Multiple Choice

Slopes of perpendicular lines are...

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

Multiple Choice

What is the slope of a line perpendicular to -10/3

• -10/3

• 10/3

• 3/10

• -3/10

Multiple Choice

What slope is parallel to:  
m = 3/4

• 4/3
• 3/4
• -3/4
• -4/3

Multiple Choice

What is the slope of a line perpendicular to 5?

• 5

• 1/5

• -1/5

• -5

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

Which figure shows a set of parallel lines?

• Figure 1
• Figure 2
• Figure 3
• Figure 4

Multiple Choice

What slope is parallel to:  
m = 4

• 4
• -1/4
• -4
• 1/4

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

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