PARALLEL AND PERPENDICULAR

LINES

What is the equation in slope intercept form of the graph:

a. y = x + 4 b. y = - x + 4

c. y = x - 4 d. y = - x - 4

What is the slope and the y-intercept of the graph:

y + 4x = -5

Write the equation of a line using the points: (-2, -4) and (2, 8).

A bird is flying at a height of 240 ft. and slowly descending at a rate of 75 ft. per second. This is represented by the equation y = 240 – 75x. What do the slope and the y-intercept represent?

PARALLEL AND PERPENDICULAR LINES IN THE REAL WORLD

In your group, you will work to complete the first part of today’s inquiry lesson (1 – 3): Discovering Parallel Lines. You will have about 10 minutes to complete this part.

• What do you notice about the lines you have drawn?

• What do you notice about the equations of the lines?

• Draw a conclusion that summarizes what you have observed. Use complete sentences.

Parallel lines

PARALLEL LINES

Line 1: y = 2x + 1

These two lines are parallel because they have the same slope. No matter how far they continue

on, they will NEVER cross each other!

Line 2: y = 2x - 3

Get ready to use your whiteboard:

• Write an equation of a line with a y-intercept of 3 that is parallel to y = - x – 4.

• Write an equation of a line that is parallel to y = 7x – 3 and passes through the origin.

• Consider the line y = x + 3. a. What is the slope of this line?b. Write a line that is parallel to it. What would the slope of

this line be?c. Determine the equation of a line parallel to this line that

passes through the point (0, - 2)

Now, complete the second section of your worksheet (7 – 12): Discovering Perpendicular Lines. You will have about 10 minutes. Be ready to articulate your ideas with the rest of the class.

• What do you notice about the intersection of each pair of lines?

• Find a pattern in the pairs of slopes for each set of lines.

• Draw a conclusion that summarizes what you have observed.

PERPENDICULAR LINES

PERPENDICULAR LINESThe red line is the graph of

y = – 2x + 5 and the blue line is the graph of

y = 1/2 x +4

These two lines are perpendicular because they have negative reciprocal slopes. They intersect at

right angles.

Get ready to use your whiteboard again:

• Write an equation of a line with a y-intercept of - 2 that is perpendicular to y = 4x + 6.

• Write an equation of a line that is perpendicular to 3x + 2y = 8 and passes through the y-intercept of that line.

• Consider the line y = x + 3. a. What is the slope of this line?b. If we drew a line perpendicular to this line, its slope would

be the opposite reciprocal of the original line’s slope. What would the slope of

the line be?c. Determine the equation of a line perpendicular to this line

that passes through the point (2, 4).

3

1m

3

1m

3

1m

31

3m

PARALLEL AND PERPENDICULAR LINES

Parallel lines have the SAME slope.

Perpendicular lines have an OPPOSITE, RECIPROCAL slope.

https://www.youtube.com/watch?v=vnnwfcDcNlY

To determine whether lines are parallel or perpendicular...

1. Write the equation in the from y = mx + b (slope intercept form)

2. Look at the slopes of the lines. • If the slopes are the same, the lines are parallel.• If the slopes are the negative reciprocals, then the

lines are perpendicular.Decide whether the following lines are parallel or perpendicular.

y = + 5 and 3x – 2y = - 16 - 2y = - 3x – 16 y = + 8These lines are parallel because they have the same slope.

Are these equations parallel or perpendicular?

On your index card, record your answer. Turn this in before you leave the room.

1. y = - + 2 and y = 3x – 5

2. y = - 4x + 1 and 4y = x + 3

3. y = 3x + 4 and y = 3x + 7

4. 4y = - 5x + 12 and y = – 8

5. 6y = - x + 6 and y = -

1. In a few sentences, describe the difference between a parallel line and a perpendicular line.

2. Give an example of parallel lines and perpendicular lines in the real world.

3. Say if the following are parallel, perpendicular or neither:a. y = 7x + 2 and x + 7y = 8b. y = 2x – 5 and y = 5x - 5

Tonight for homework you will start working on your review sheet for the upcoming test.

Use your notes and the power points on my wiki to help.

Use the videos on the Homework Help slides if you need to see something visual.

Homework Help

https://www.youtube.com/watch?v=Rew54K6mYUo

https://www.youtube.com/watch?v=SgJDyIs9b2A

https://www.youtube.com/watch?v=09ZpC614laQ