Section 4.2E: Parallel and Perpendicular Lines Teacher Notes
Find the x and y intercepts of each equation:
1.) 2x – 4y = 12
2.) 5x + 20y = 10
x = (6, 0); y = (0, -3)
x = (2, 0); y = (0, 0.5)
Objective: Students will be able to determine whether lines are parallel or perpendicular.
Vocabulary
1.) Parallel Lines – lines in the same plane that never intersect
2.) Perpendicular Lines – lines that intersect to form right angles
3.) Opposite reciprocals – two numbers whose product is -1 (one number is opposite
the other number and is the reciprocal of the other)
Lines are Parallel if they have:
1.) The same slope
2.) Different y-intercepts
Lines are Perpendicular if:
1.) The product of their slopes is -1 (the slopes are negative reciprocals of each
other)
Examples
Are the lines parallel, perpendicular, or neither?
3
1.) y =  x + 2 and 3x + 2y = 8
2
3
y=  x+2
3x + 2y = 8
2
2y = -3x + 8
3
y=  x+4
2
3
3
Slope = 
Slope = 
2
2
Yes the lines are parallel because they have the same slope and different y -intercepts.
3
2.) y = 4x +
and x + 4y = 16
4
3
y = 4x +
x + 4y = 16
4
4y = -1x + 16
1
y =  x + 16
4
1
Slope = 4
Slope = 
4
Yes, the lines are perpendicular because the product of the slopes is -1 and the slopes
are opposite reciprocals of each other.
3.) y = -5x and y = 5x + 7
Slope = -5 and Slope = 5
Parallel: No, not the same
Perpendicular: No, not the
opposite reciprocals
Neither
4.) Which lines are parallel? Justify your answer.
3
3
1
6
Line B: Slope =  3
2
4
Line C: Slope =  4
1
Line A: Slope =
Lines A & B are parallel because they have the same slope and different y-intercepts.