5-8
Slopes of Parallel and
Perpendicular Lines
Learning Target
Students will be able to: Identify and graph
parallel and perpendicular lines and write
equations to describe lines parallel or
perpendicular to a given line.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
To sell at a particular farmers’ market for a year,
there is a $100 membership fee. Then you pay $3
for each hour that you sell at the market. However,
if you were a member the previous year, the
membership fee is reduced to $50.
• The red line shows the
total cost if you are a
new member.
• The blue line shows the
total cost if you are a
returning member.
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
These two lines are parallel.
Parallel lines are lines in
the same plane that have
no points in common. In
other words, they do not
intersect.
l1 // l 2  l1 & l 2 have the sam e slope
and different y -intercepts
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Identify which lines are parallel.
l4  y  1  3 x  9
l1  y  2 x  3
l4  y  3 x  1 0
2
l2  y   x  3
3
l3  2 x  3 y  8
2
3
l // l
2 x
3 y  2 x  8
3
3
3
2 x
l3  y  
Holt Algebra 1
2
3
x
y = 2x – 3
8
3
y + 1 = 3(x – 3)
5-8
Slopes of Parallel and
Perpendicular Lines
Identify which lines are parallel.
y = 2x + 2; y = 2x + 1; y = –4; x = 1
l1  y  2 x  2
l2  y  2 x  1
l3  y  0 x  4
l4  x  1
y = 2x + 2
y = 2x + 1
l1 // l 2
l3  l 4
Holt Algebra 1
y = –4
x=1
5-8
Slopes of Parallel and
Perpendicular Lines
Show that JKLM is a parallelogram.
m ML  0
m JK  0
m JM 
m KL 
Holt Algebra 1
4
1
4
1
4
4
JK L M is a //ogram
because opposite sides are //.
5-8
Slopes of Parallel and
Perpendicular Lines
Show that the points A(0, 2), B(4, 2), C(1, –3),
D(–3, –3) are the vertices of a parallelogram.
m AB  0
m 
mCD  0
m AD 
m BC 
Holt Algebra 1
3  2
3  0
3  2
1 4
y 2  y1
A B C D is a //ogram
x 2  x1
because opposite sides are //.


5
3
5
3


5
A(0, 2)
3
5
3
D(–3, –3)•
•
B(4, 2)
•
• C(1, –3)
5-8
Slopes of Parallel and
Perpendicular Lines
Perpendicular lines are lines that intersect to
form right angles (90°).
 slopes are negative reciprocals
i .e . m 1  
Holt Algebra 1
1
m2
5-8
Slopes of Parallel and
Perpendicular Lines
Identify which lines are perpendicular: y = 3;
x = –2; y = 3x;
.
y  3  x  2
x = –2
y  3x  y  
1
3
 x  4
y =3x
Holt Algebra 1
y=3
5-8
Slopes of Parallel and
Perpendicular Lines
Show that ABC is a right triangle.
A B C is a R ight 
because m  B A C  90 .
m AB 
20
1   2 
m AC 
Holt Algebra 1
3  0
0   2 

2

3

2
3
3
2

3
2
m 
y 2  y1
x 2  x1
5-8
Slopes of Parallel and
Perpendicular Lines
Write an equation in slope-intercept form for
the line that passes through (4, 10) and is
parallel to the line described by y = 3x + 8.
y  mx  b
1 0    3   4   b
10  12  b
b  2
Holt Algebra 1
y  3x  2
5-8
Slopes of Parallel and
Perpendicular Lines
Write an equation in slope-intercept form for the
line that passes through (2, –1) and is
perpendicular to the line described by y = 2x – 5.
y  mx  b
 1
  1      2   b
 2
1  1  b
y
b  0
Holt Algebra 1

1
2
x
5-8
Slopes of Parallel and
Perpendicular Lines
HW: 5.8 Reteach WS & Unit Review
Holt Algebra 1
5-8
Slopes of Parallel and
Perpendicular Lines
Warm Up
Find the reciprocal.
1. 2
2.
3
3.
Find the slope of the line that passes through
each pair of points.
4. (2, 2) and (–1, 3)
5. (3, 4) and (4, 6)
6. (5, 1) and (0, 0)
Holt Algebra 1
2
5-8
Slopes of Parallel and
Perpendicular Lines
Find the 25th term of the arithmetic sequence.
a1 = –5; d = –2
a n  a1   n  1  d
a n   5   n  1   2 
a 2 5   5   2 5  1    2    5   24    2 
  5  48
 53
Holt Algebra 1