# Activity 4.4.6 Parallel and Perpendicular Lines

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Parallel &amp; Perpendicular Lines
1. Jason and Scott plan on biking to the center of town to get ice cream at the convenience
store. Since Scott had to put air in his tires, Jason was able to get 1 mile ahead of Scott
before Scott left the house. Both bikers rode at a speed of 15 miles per hour.
a. Write an equation in y  mx  b form that represents Jason’s trip.
b. Write an equation in y  mx  b form that represents Scott’s trip.
c. Will Jason and Scott meet before they both reach the store? Explain.
d. If you were to graph both lines on the same coordinate plane, predict what your graph
would look like.
2. a. On the same set of axes graph the following lines. Use a ruler to make your lines.
y = 3x + 4
y = 3x  4
y = 3x
y
x
Activity 4.4.6
CT Algebra I Model Curriculum Version 3.0
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b. What do you notice about the lines you graphed in problem 2?
c. What can you say about the slopes of parallel lines?
3. a. On the same set of axes graph the following lines. Use a ruler to make your lines.
y
y  2x  1
y
1
x 1
2
x
1
b. How does the line 𝑦 = 2𝑥 + 1 compare to 𝑦 = − 2 𝑥 − 1? Discuss the slopes of each
line and what type of angle is formed where the lines intersect.
Activity 4.4.6
CT Algebra I Model Curriculum Version 3.0
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4. a. On the same set of axes graph the following lines. Use a ruler to make your lines.
y
y
y
2
x4
3
3
x3
2
x
2
3
b. How does the line 𝑦 = − 3 𝑥 + 4 compare to 𝑦 = 2 𝑥 − 3? Discuss the slopes of each
line and what type of angle is formed where the lines intersect.
Perpendicular lines have slopes that are opposite reciprocals of each other.
For example, what is the opposite reciprocal of 6?
Step 1  Take the 6 and write it as a fraction
6
1
Step 2  Flip it over (also known as the reciprocal)
1
6
Step 3  Change the sign (also known as the opposite) 
Therefore, the opposite reciprocal of 6 is 
1
6
1
.
6
5. Find the opposite reciprocal of each number.
a. -4
Activity 4.4.6
b.
5
2
c. 
3
7
d. 0
CT Algebra I Model Curriculum Version 3.0
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6. Below are the equations of four lines.
1
y   x7
5
y
1
x 8
5
y  5 x  6
1
y   x8
5
a. Which pairs of lines are parallel?
b. Which pairs of lines are perpendicular?
7. Write the equation of a line parallel to the given line. Note: There is more than one correct
a.
y  4 x  1 is parallel to
b.
y  9 x  2 is parallel to
c.
5
y   x  2 is parallel to
6
d.
y
1
x  11 is parallel to
2
8. Write the equation of a line perpendicular to the given line. Note: There is more than one
a.
y
4
x  1 is perpendicular to
3
b. y  9 x  13 is perpendicular to
c.
y
1
x  6 is perpendicular to
7
3
7
d. y   x  4 is perpendicular to
Activity 4.4.6
CT Algebra I Model Curriculum Version 3.0
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9. Summarize what you have learned in this activity. Fill in the blank of each statement or
circle the appropriate word to make the statement true.
a. Parallel lines have the _________________________ slope.
b. Parallel lines have (same, different) y-intercepts.
c. Parallel lines ________________________________ intersect each other.
d. Two lines with slopes that are ______________________________ reciprocals of each
other are perpendicular to each other.
e. Perpendicular lines have (same/different) y-intercepts.
f. A pair of perpendicular lines intersects at _________________________ angle.
Activity 4.4.6
CT Algebra I Model Curriculum Version 3.0
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