Parallel and
Perpendicular Lines
Chapter 3, Section 5
Video
 https://www.youtube.com/watch?v=Rew54K6mYUo
Lesson and Notes
 Slope of Parallel and Perpendicular Lines
Practice Review: Write the equation of a line from a graph.
-2
+4
+4 =-2
-2
Parallel lines
Lines in the same
plane that do not
intersect are called
parallel lines.
Parallel lines have
the same slope.
10
1
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9
– 10
1
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1– 10
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9
10
1
2
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8
9
Notes: Write the equation of a parallel line
y
10
9
8
7
6
5
4
3
2
1
– 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
1
2
3
4
5
6
7
8
9 10
x
Practice. Write the equation of a parallel line.
Write the equation of a line parallel to the line shown
below and passing through point (1, 2)
(1, 2)
M=2/3 and b is -1 so
-2
Y-intercept
Step 2: Substitute into y = mx + b
2  1 (1 )  b
-3
1 b
M =-2 = 2
-3 3 The slope is 2/3, the y-intercept is 1,
so the equation of the parallel line is
y=2/3x+1
Practice: Write the equation of a parallel line.
10
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– 10
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1– 10
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9
10
1
2
3
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6
7
8
9
y
Substitute point (1,5) and the
slope (3) into y=mx+b
5  3 (1 )  b
10
M= 3
1
9
8
7
+1
6
5
+3
4
3
Y-intercept
2
1
+1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
5  3b
1
2
3
4
5
6
7
8
–2
–3
+3
–4
–5
2b
–6
–7
–8
–9
– 10
Y-intercept
9 10
x
Perpendicular Lines
Opposite reciprocals????
Lines that intersect at
right angles are
called
perpendicular lines.
The slopes of these
lines are opposite
reciprocals.
3…..
1
3

1
4
...
4
10
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– 10
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1– 10
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8
9
Write the equation of a perpendicular line.
Graph the lines.
y
10
9
8
7
6
5
Y-intercept
-2
4
3
2
1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
1
+1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
2
3
4
5
6
7
8
9 10
y
10
9
Flip the slope over and change the sign
to the opposite. If the original slope is
positive, the new one will be negative.
If the original is negative, the new one
will be positive.
(y=7/3)x+10
8
7
6
5
4
3
2
1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
–2
–3
–4

7
3

3
–5
–6
–7
7
–8
–9
– 10
1
2
3
4
5
6
7
8
9 10
x
1– 10
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3
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7
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9
10
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2
3
4
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7
8
9

3
y
10
9
7
Plug the new slope and the point
(-1, 1) into y = mx +b
(y=7/3)x+10
8
7
6
5
4
-7
3
y  
3
7
x
4
2
1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
7
–2
–3
–4
–5
–6
–7
–8
–9
– 10
1
2
3
4
5
6
8 9
+3
7
10
x
10
Group Activity
(click for answers)
9
8
7
6
5
4
3
2
1
– 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
1
2
3
4
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9
10
x
10
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2
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– 10
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1– 10
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9
Practice: Writing Equation of a Perpendicular Line
y
10
9
8
7
6
5
4
-3
3
+1
2
1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
1
2
3
4
5
6
7
8
9 10
x
Practice: Writing Equation of a Perpendicular Line
y
10
9
8
7
6
5
4
3
2
1
– 10– 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1
–1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
1
2
3
4
5
6
7
8
9 10
x
Notes: Solutions
Quiz
http://www.classzone.com/etest/viewTestPractice.htm?te
stId=4498
http://www.classzone.com/etest/viewTestPractice.htm?testI
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