Equations of Parallel and Perpendicular Lines
Name ______Module 4
Equations of Parallel and Perpendicular Lines
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) y=12x-5
(2) y=-12x+4
(3) y=-2x+6
(4) y=2x+8
3. Which equation represents a line parallel to the x-axis?
(1) x=5
(2) y=10
(3) x=13y
(4) 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 12 and centered at the origin. What is the equation that represents the image of the line after the dilation?
Name ______Module 4
Equations of Parallel and Perpendicular Lines Problem Set
1. Which equation represents a line parallel to the y-axis?
(1) x=y
(2) x=4
(3) y=4
(4) y=x+4
2. Which equation represents a line that is parallel to the line y=3-2x?
(1) 4x+2y=5
(2) 2x+4y=1
(3) y=3-4x
(4) y=4x-2
3. The line y = 2x – 4 is dilated by a scale factor of 32 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
to y=35x+2.
7. Write the equation of a line that passes through the point (3,54) and is parallel
to 12x-34y=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 contains points (−4,2) and (−2,9). Line contains points (,−1) and (−1,1).
a. Find the value of if the lines are parallel.
b. Find the value(s) of if the lines are perpendicular.
11. Find the distance between the point (0,0) and the line y=x+10.
Name ______Module 4
Equations of Parallel and Perpendicular Lines Exit Ticket
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.