MPM 2D0
Parallel and Perpendicular Lines
1. For each of the given slopes, find the slope of a line parallel to that line, and the slope of a line
perpendicular to that line.
1
2
a) m = 2
b) m =
c) m = –3
d) m =
e) m = –6
4
3
2. Given the slopes of two lines, determine whether the lines are parallel, perpendicular or neither.
1
2
7
a) m1 = 3 and m 2 =
b) m1 = m 2 =
c) m1 = 1 m 2 = –1
4
7
2
d) m1 =
2
4
m2 =
6
12
e) m1 = –3 m 2 =
1
3
3. Identify whether each pair of lines is parallel, perpendicular, or neither.
1
a) y  2 x  5 and y  2 x  1
b) y  x  3 and y  2 x  3
2
c) y  3x  1 and y  3x  1
d) y  x  5 and y   x  4
4. Find the slopes of each of the following lines. Then, classify them as parallel, perpendicular or neither.
a) Line 1: (–2, 8), (3, 7)
Line 2: (4, 3), (9, 2)
b) Line 1: (0, 1), (–5, 4)
Line 2: (5, 3), (0, 5)
c) Line 1: (2, 5), (8, 7)
Line 2: (–3, 1), (–2, –2)
d) Line 1: (4, 6), (–3, –1)
Line 2: (6, –3), (4, 5)
5. Find the equation of the line, in slope-intercept form, for each of the following:
a) through (4, 6) and parallel to y = 3x + 4
b) through (–2, –3) and parallel to y +2x = 6
c) through (–1, 5) and perpendicular to y = –3x +7
d) through (–3, –2) and perpendicular to y – 2x + 6 = 0
e) through (5, 2) and parallel to 3x – 5y = 6
f) having the same x-intercept as 3x + 5y – 15 = 0 and parallel to 5x + 2y = 17
g) having the same y-intercept as 2x – 3y = –6 and perpendicular to 4x – y = 6
Parallel and Perpendicular Lines – SOLUTIONS
1.
Parallel Slope
Perpendicular Slope
1

2
a)
2
b)
1
4
–4
c)
–3
d)

e)
–6
1
3
3
2
1
6
2
3
2. a) Neither
b) Neither
c) Perpendicular
d) Parallel
3. a) Parallel
b) Perpendicular
c) Neither
d) Perpendicular
1
1
4. a) m1   , m2  
5
5
1
c) m1  , m2  3
3
5. a) y  3x  6
e) y 
3
x 1
5
e) Perpendicular
Parallel
3
2
b) m1   , m2  
5
5
Neither
Perpendicular
d) m1  1, m2  4
Neither
1
16
x
3
3
b) y  2 x  7
c) y 
5
25
f) y   x 
2
2
1
g) y   x  2
4
1
7
d) y   x 
2
2