Math 10C

Chapter 7 Linear Equations and Graphs

Lesson 74 Parallel and Perpendicular Lines

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 383

Read/Work through the  Focus  section at the top of page 383 in  your textbook.

Football... perpendicular...?   
See the second diagram on THIS PAGE   (How to throw a perfect spiral)

Investigate

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 383 - 384

Read/Work through the  Investigate  section on Pages 383 - 384 in your textbook.

A list of materials  you need for the Investigation is given in the side bar.

Your work will be a lot more efficient if you PLAN for and GATHER these items BEFORE you start the Investigation!

You may not have other students to work with.  
No worries!  
If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video for help with this section.

Watch

Video Tutorial 1

Video Tutorial 2

Video Tutorial 3

Video Tutorial 4

Video Tutorial 5

Video Tutorial 67 (questions 6 and 7)

I answered question 8 as I was doing the previous questions.

Demonstration

In the following demonstration,  you can click and drag the locators (points)  to anywhere ON THE GRID.

The points will snap to lattice locations (locations on the grid).

This just made it easier to see when the lines were either parallel or perpendicular.

Move the points to several different locations and experiment with creating parallel or perpendicular lines.
(or, if you DID the Investigation, you can CONFIRM what you now know....)

When you are done you should hopefully have an understanding of how the slopes  of two parallel lines are related, and how the slopes  of two perpendicular lines are related.

When the lines are Parallel,  the word Parallel will appear (go figure...)

When the lines are Perpendicular (at 90° to each other),  the word Perpendicular will appear  (I'm not making this up....)

If the lines are neither parallel nor perpendicular,  the word OBLIQUE will appear.

The big ideas

Parallel Lines

If two lines are parallel,  their slopes are equal

(or they are both vertical)

Parallel Lines  (Open Math Reference)  »

Perpendicular Lines

If two lines are perpendicular,  their slopes are negative reciprocals  (opposite and flipped)

(or one line is vertical and the other is horizontal)

Perpendicular Lines  (Open Math Reference)	  »

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 385

Read/Work through the  Link the Ideas  section on Page 385 in your textbook.

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Identify Parallel and Perpendicular Lines

TEXT Pages 386 - 387

Work through Example 1 on Pages 386 - 387 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Write an Equation Involving a Parallel Line

TEXT Pages 387 - 388

Work through Example 2 on Pages 387 - 388 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Write an Equation Involving a Perpendicular Line

TEXT Page 389

Work through Example 3 on Page 389 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Practice questions require basic understanding of the ideas of the  lesson.

Apply questions will require you to dig deeper for a solution.

Extend questions offer enrichment and extension.

Create Connections questions connect the math to everyday contexts.

Mini Lab (optional)  your teacher may or may not have you do these.

Notes

Question 16,    HERE is the link to the Desmos graph I used in my answer.

Question 19,   HERE is the link to the Desmos graph I used in my answer.

Question 20,    HERE is the link to the Desmos graph I used in my answer.

Question 24,    HERE is the link to the Desmos graph I used in my answer.

Question 26,    I didn’t do a video for this one.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, {"Question 16", "Question 17", "Question 18", "Question 19", "Question 20"}, {"Question 21", "Question 22", "Question 23", "Question 24", "Question 25"}})