Transcript Writing Parallel and Perpendicular Lines

Writing Parallel
and
Perpendicular Lines
Part 1
Parallel Lines
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//
(symbol)
All parallel lines have the same slope.
Parallel lines will NEVER CROSS.
Since Parallel lines don’t cross, we say they have
NO solution.
The slope of all vertical lines is undefined. (No
Slope)
The slope of all horizontal lines is zero.
Given slope:
Parallel slope:
2
A) y = x  7
3
2
m
3
B) y = 4x  8
m4
C ) y =  5x  3
m  5
7
D) y =
x4
15
7
m
15
1) Find line parallel to y = 6x  4 and goes
through (-6, 4)
( x1 , y1 )
Step 1
Step 2
Step 3
Find m
Find b
Find equation
Plug in x,y, & m
Plug in m & b
From
given eq.
y  mx  b
y  6x  4
m6
now go to
next column
4  6(6)  b
4  36  b
36 36
40  b
y  mx  b
6 x 40
y  __
__
y  6 x  40
3 x  8 y  8
2) Find line parallel to
through (6, -2)
Step 2
Step 1
(
x
,
y
)
Find b
1
1
Find m—
Plug in x,y, & m
solve for y
y  mx  b
From given eq.
3 x  8 y  8 2  3 (6) b
3x
3x (8) (8)8
18 (8)

8 y  3 x  8
8 3 8
8
y
8
x 1
3
m
8
now go to next column
2 
8
16  18
18 18
2
8

 8b
 8b
1
4
b
8
b
and goes
Step 3
Find equation
Plug in m & b
y  mx  b
1
3
4
8 x  __
y  __
3
1
y
x
8
4
Perpendicular Lines (symbol)
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

Lines that form a 90° Angle.
Perpendicular Lines have one solution written as an
ordered pair.
Perpendicular Lines’ slopes are NOT the same
(negative reciprocals).
Do 2 things…
FLIP the slope
&
CHANGE the SIGN
3
m
2
2
m
3
Given slope:
5
A) m 
6
1
B) m 
3
Perpendicular
slope:
6
m
5
3
m
 3
1
4
C) m 
7
7
m
4
D) m  9
1
m
9
3) Find line perpendicular to
through (-6, 4)
1
y = x+4 and goes
3
( x1 , y1 )
Step 1
Step 2
Step 3
1
y  x4
3
4  3(6)  b
4  18  b
18 18
14
y 
__3x __
FLIP the slope
&
CHANGE the SIGN
3
m
 3
1
now go to next
column
14  b
y  3 x  14
4) Find line perpendicular to
goes through (4, 7)
Step 1
( x1 , y1 )
5 x  2 y  10
5x
5x
FLIP the slope
&
CHANGE the SIGN
2
m
5
now go to next column
Step 2
5
(5)
7
8
5
35  8
(5)

27
5
b
 5b
8 8
27  5b
5
5
b
and
Step 3
y  mx  b
2
7  (4)  b
2 y  5 x  10
(5)
2
2
2
5
y
x5
2
2 x  5 y  10
y  mx  b
27
2
5
5 x  __
y  __
2
27
y  x
5
5