Lesson 3: Parallel and Perpendicular Lines
Module 6: Linear Equations
Try This 3 - 4
Complete the following in your binder to practice identifying parallel and perpendicular lines.
Try This 3 - 4 Questions
Use the link below to check your answers to Try This 3 -4.
Possible TT3-4 Solutions
Read
Go to your textbook to find examples of how to identify both parallel and perpendicular lines.
Foundations and Pre-calculus Mathematics 10 (Pearson)
Read “Example 1: Identifying Parallel Lines” on page 345. Next, read “Example 2: Examining Slopes to Compare Lines” on pages 346 and 347.
Before you look at the solutions to both of these examples, try to figure out the answers by studying the graphs. How important do you think it is to sketch a graph of the problem before trying to solve it?
Watch and Listen
Use “Parallel and Perpendicular Line Segments Applet” as a way to check your understanding of the slopes of parallel lines and perpendicular lines. Scroll down to find the applet. Choose Parallel lines only first and then once you have played around for a while, choose Perpendicular lines only and play with that. Once you move a point, look to see what that does to the lines and in particular the slopes of the lines.
Once you have played with the applet, if you feel you need more work on this, scroll back UP to the top and click on the Parallel and Perpendicular Lines lesson for more solved examples.
Try This 5
Complete the following in your binder.
TT5: Foundations and Pre-calculus Mathematics 10 (Pearson)
a. Complete “Exercises” questions 5, 6, 8.a), 8.b), 9.b), 9.c), and 17 on pages 349 and 350.b. Complete “Exercises” question 21 on page 364.
Use the link below to check your answers to Try This 5.
Possible TT5 Solutions
Let's have a look at an application question to help us work on our understanding of parallel and perpendicular lines.
Example 3:
For the pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?
Solution:
When lines are parallel, their slopes are equal, so we can equate the slopes and solve.
When lines are perpendicular, the slopes are negative reciprocals. So the number of the right of 2 needs to be reciprocated and made a -1/2.
In previous lessons you learned how to write the equation of a linear function. You learned that you need to know the slope of the function as well as a point on the graph. These pieces of information are not always given directly.
For example, you have seen that you may have to use two points to determine a slope before you can write the equation of a line. You can also indirectly determine the slope of a line by using the given information about another line that is either parallel or perpendicular.
Example 4:
Write the equation of a line that passes through (1, 2) and is parallel to the line 2x - 3y + 10 = 0. Write the final answer in slope intercept form and general form.
Solution:
Step 1: Change the given line into slope intercept form, so the slope can be found:
Step 2: Use slope point form and find the equation in slope intercept form.
Step 3: Change slope intercept form to correct general form. ( remember, no fractions and A has to be positive)
Read
Go to your textbook to work through examples on how to write the equations of lines that are parallel or perpendicular to given lines.
Foundations and Pre-calculus Mathematics 10 (Pearson)
As you read the textbook example, try to answer the questions:
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In what form(s) is the slope of the line easiest to determine?
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How could you continue the work in the example to find the y-intercept?
Read “Example 4: Writing an Equation of a Line That Is Parallel or Perpendicular to a Given Line” on page 370.
Self-Check
SC 3. Write the equation of a line parallel to the line y = 2x − 1 and that passes through (−5, 1).
SC 4. Write the equation of a line that passes through the point 
and is perpendicular to the line 
Compare your answers to SC3 and 4.
SC 5. For the pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?
Compare your answers to SC5
Watch and Listen
For more help on finding equations of parallel and perpendicular lines, watch this screen cast. There are also solved examples on the bottom left.
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Try This 6
Complete the following in your binder.
Foundations and Pre-calculus Mathematics 10 (Pearson)
TT 6. Complete “Exercises” questions 20, 22, 24, 25, and 26 on page 374.
Use the link below to check your answers to Try This 6.
Possible TT6 Solutions