Name ______________________________
Equations of Parallel and Perpendicular Lines
Module 4
Learning Target: I can apply slope criteria for parallel and perpendicular lines and use them to solve
geometric problems.
Opening Exercises
1. What is the slope of the line passing through the points A and B, as shown on the graph below?
2. Write the equation of the line graphed below.
Equations of Parallel and Perpendicular Lines
Essential Understanding: Parallel lines have equal slopes.
1. Determine the slope of each line to show that the lines are parallel.
2. Which equation represents a line parallel to the graph of 2𝑥 − 4𝑦 = 16?
1
(1) 𝑦 = 2 𝑥 − 5
1
(2) 𝑦 = − 2 𝑥 + 4
(3) 𝑦 = −2𝑥 + 6
(4) 𝑦 = 2𝑥 + 8
3. Which equation represents a line parallel to the x-axis?
(1)
(2)
(3)
(4)
𝑥=5
𝑦 = 10
1
𝑥 = 3𝑦
𝑦 = 5𝑥 + 17
4. Write an equation of the line that passes through the point (4,2) that is parallel to the line whose
equation is 3𝑥 + 6𝑦 = 12.
Essential Understanding: The slopes of perpendicular lines are negative reciprocals.
5. What is the slope of a line perpendicular to the line 𝑦 = 5𝑥 − 4?
6. Write an equation of the line that passes through the point (4,2) that is perpendicular to the line
whose equation is 3𝑥 + 6𝑦 = 12.
7. Find the distance between the point (0,0) and the line 𝑦 = −𝑥 + 4.
Essential Understanding: A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
A. Graph the equation on the line that passes through the points 𝐴(−4,8) and 𝐵(4,6).
B. What is the equation of the line passing through the points A and B, as shown on the graph above?
C. The line that passes through the points A and B is dilated by a scale factor of
1
2
and centered at the
origin. What is the equation that represents the image of the line after the dilation?
Name ______________________________
Equations of Parallel and Perpendicular Lines
Module 4
Problem Set
1. Which equation represents a line parallel to the y-axis?
(1)
(2)
(3)
(4)
𝑥=𝑦
𝑥=4
𝑦=4
𝑦 =𝑥+4
2. Which equation represents a line that is parallel to the line 𝑦 = 3 − 2𝑥?
(1)
(2)
(3)
(4)
4𝑥 + 2𝑦 = 5
2𝑥 + 4𝑦 = 1
𝑦 = 3 − 4𝑥
𝑦 = 4𝑥 − 2
3
3. The line y = 2x – 4 is dilated by a scale factor of 2 and centered at the origin. Which equation
represents the image of the line after the dilation?
(1) y = 2x – 4
(2) y = 2x – 6
(3) y = 3x – 4
(4) y = 3x – 6
4. The equation of line h is 2𝑥 + 𝑦 = 1. Line m is the image of line h after a dilation of scale factor 4
with respect to the origin. What is the equation of the line m?
(1) y = –2x + 1
(2) y = –2x + 4
(3) y = 2x + 4
(4) y = 2x + 1
5. If the graphs of the equations 𝑦 − 2𝑥 and 𝑦 − 𝑘𝑥 = 7 are parallel, what is the value of k?
6. Write the equation of a line that passes through the point (−5,3) and is perpendicular
3
to 𝑦 = 5 𝑥 + 2.
5
7. Write the equation of a line that passes through the point (√3, 4) and is parallel
1
3
to 2 𝑥 − 4 𝑦 = 10.
8. Are the lines 4𝑥 − 9𝑦 = 8 and 18𝑥 + 8𝑦 = 7 parallel, perpendicular, or neither? Explain.
9. Are the lines 3𝑥 + 2𝑦 = 74 and 9𝑥 − 6𝑦 = 15 parallel, perpendicular, or neither? Explain.
10. Line 𝐴 contains points (𝑝−4,2) and (−2,9). Line 𝐵 contains points (𝑝,−1) and (−1,1).
a. Find the value of 𝑝 if the lines are parallel.
b. Find the value(s) of 𝑝 if the lines are perpendicular.
11. Find the distance between the point (0,0) and the line 𝑦 = 𝑥 + 10.
Name ______________________________
Equations of Parallel and Perpendicular Lines
Write the equation of the line that contains the point (−2,7) and is
a. Parallel to 𝑥 = 3.
b. Perpendicular to 𝑥 = −3.
c. Parallel to 𝑦 = 6𝑥 − 13.
d. Perpendicular to 𝑦 = 6𝑥 − 13.
Module 4
Exit Ticket