Parallel and Perpendicular Lines

Multiple Select

I expect the following (please check to acknowledge each expectation)

• You must read each slide, and you should take your time

• You should take notes

• It is possible this Quizizz lesson will take the entire period

• Talking is no more than a whisper unless you substitute says "no talking"

Equations of Parallel and Perpendicular Lines
and a Review of Other Equations

​

​Parallel Lines

Each walks....​
1 block North
2 blocks East

​Friends never cross paths

Equations of Parallel and Perpendicular Lines
and a Review of Other Equations

​Parallel Lines

Rise = 1

​Run =2

Rise = 1

​Run =2

Match

Match the following:

• Parallel lines' slopes

• Parallel lines' y-intercepts

• Parallel lines' solutions

Same

Different

None

• Same

• Different

• None

Parallel Lines

To determine if two equations will result in parallel lines........

• Ensure both equations are in slope-intercept form (y=mx+b)

• Compare the slopes (m)

• Compare the y-intercepts (b)
  

Parallel Lines

Consider the following equations:

• y = 3x + 8

• -3x + y = 10

  
  

​Before we can compare slopes and y-intercepts, both equations have to be in slope-intercept form

Multiple Choice

y=3x+8 is in proper slope-intercept form

-3x+y=10 is not in proper slope-intercept form

• True

• False

Parallel Lines

Let's make the equation -3x + y = 10 more accessible by putting it in slope-intercept form:

​-3x + y = 10
+3x +3x Move the variable
y = 3x + 10

​So, the two equations, now in slope-intercept form, are:
y = 3x + 8
y = 3x + 10

Drag and Drop

Now compare the slopes and y-intercepts of the following equations:

y = 3x + 8 y = 3x + 10



The slope of the first equation is ​

Placeholder

. The slope of the second equation is 3.

The y-intercept of the first equation is​

Placeholder

, and the y-intercept of the second equation is ​

Placeholder

Drag these tiles and drop them in the correct blank above

3

8

10

3x

-3x

x

(10,0)

Parallel Lines

Since both equations have the same slope, m=3, and since the equations have different y-intercepts, b=8 and b=10.....

The lines are parallel

y = 3x + 8
y = 3x + 10

The lines are parallel

​These lines will never intersect. There is no solution to the System of Equations.

Perpendicular Lines

Now, let's talk about perpendicular lines! What do you think perpendicular means?

Perpendicular Lines

​Two lines that form a 90 degree, right angle at the point of intersection

Perpendicular Lines

​Think about what the slopes and
y-intercepts may look like for these
two lines when compared

Slopes are opposite

Opposite

Slopes are reciprocal

​​Reciprocal

​Slopes of Perpendicular Lines

Match

Match the opposites:

• 3

• 2,015

• $$\frac{1}{12}$$

• $$87^2$$

• (x+8)

-3

-2,015

-(x+8)

• -3

• -2,015

• $$-\frac{1}{2}$$

• $$-87^2$$

• -(x+8)

That exercise was simple, right???

Now, what do you call about reciprocals?

Slopes are opposite

Opposite

Slopes are reciprocal

​​Reciprocal

​Slopes of Perpendicular Lines

Perpendicular Lines

​Reciprocals

Match

Match the following reciprocals:

• $$\frac{2}{3}$$

• $$-\frac{2}{3}$$

• $$\frac{3a}{2}$$

• $$-\frac{3a}{2}$$

• $$\frac{3}{2}$$

• $$-\frac{3}{2}$$

• $$\frac{2}{3a}$$

• $$-\frac{2}{3a}$$

Perpendicular
Lines

Perpendicular lines have slopes that
are both opposite reciprocals​

​Equations:
If Line A has the following equation: y = 5x - 2
then what would the slope need to be for Line B in order for the lines to intersect at a 90 degree angle (to be perpendicular)?

Perpendicular
Lines

Perpendicular lines have slopes that
are both opposite reciprocals​

Perpendicular
Lines

these lines are perpendicular. slopes are
opposite reciprocals. notice the lines intersect at a 90 degree angle

Match

Let's see what you know about perpendicular lines. Match the true statements!

• Slopes

• Intersect

• Type of intersection

• One slope is positive, and one slope is...

• If the slope of Line A is 6, the slope of Line B is specifically....

Opposite reciprocals

Always

90 degrees

Negative

• Opposite reciprocals

• Always

• 90 degrees

• Negative

• $$-\frac{1}{6}$$

Perpendicular Lines

Perpendicular Lines

Match

Match the slopes with the appropriate equations

• $$y=3x+5$$

• $$y=-7x-3$$

• $$y=\frac{2}{3}x+17$$

• $$m\ =\ 3$$

• $$m=\ -7$$

• $$m=\frac{2}{3}$$

Fill in the Blanks

Math Response

$$y\ =\ 3x\ +5$$

The opposite slope is -3

What is the slope of the equation that creates a line that is perpendicular to the line's equation above?

(-Hint: Perpendicular lines have opposite reciprocal slopes)

Type answer here

Correct Answer: -\frac{1}{3}

Deg^°

Rad

Perpendicular Lines

Perpendicular Lines

Categorize

Options (15)

Always same slopes

Always different y-intercepts

Opposite, reciprocal slopes

$$y=4x,\ y=-\frac{1}{4}x$$  

$$y=3x+2,\ y=3x-40$$  

$$y=2x,\ y=-\frac{1}{2}x$$  

$$m=4,\ m=4$$  

$$m=-\frac{p}{q},\ m=\frac{q}{p}$$  

System of Equations has no solution

System of Equations has one solution

Infinite, many solutions

90 degree angle intersection

y=-x+8, y=-x+12

Categorize the following characteristics with the appropriate types of lines:

Parallel Lines

Perpendicular Lines

Exact Lines

Intersecting Lines (not perpendicular)

Ready to be Quizzed ??

Dropdown

These perpendicular lines:

1.​

Select answer

at a 90 degree angle

2. Have ​

Select answer

reciprocal ​ slopes​

Fill in the Blanks

Multiple Choice

The lines are parallel:

The equation for the first line is y = -x + 12

The equation for the second line is:

• y = -1

• $$y\ =\ \frac{1}{8}x\ +\ 8$$

• y= -x + 8

• y = x + 8

Multiple Choice

Parallel lines must have different y-intercepts

• True

• False

Reorder

Perpendicular Lines: Consider the following equation, and put the slides in order:

$$y\ =\ \frac{3}{2}x\ -\ 9$$

Slide 1 Slope of the equation above

Slide 2 Opposite slope of the equation above

Slide 3 Reciprocal of the slope above

Slide 4 Opposite reciprocal of the equation above

• $$\frac{3}{2}$$

• $$-\frac{3}{2}$$

• $$\frac{2}{3}$$

• $$-\frac{2}{3}$$

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Select

Select all that are true:

Perpendicular Lines.......

• Never intersect

• Always intersect

• Intersect at every point on both lines

• Form a 90 degree angle at the point of intersection

Multiple Select

Select all that are true:

Parallel Lines.......

• Never intersect

• Always intersect

• Always have the same slopes

• Always have different y-intercepts

Multiple Choice

Which equation creates a perpendicular line to:

$$y\ =\ -\frac{1}{1}x\ +4$$

• $$y\ =\ x$$

• $$y\ =\ 4x$$

• Always have the same slopes $$y\ =\ \frac{1}{1}x\ +\ 4$$

• $$y\ =\ \frac{1}{4}x\ +\ 4$$

After completing Quizizz:

There are paper copies of problems on the podium

​Practice on Paper

Any 8th grade IXL

​Work on IXL