Download 7_8 TROUT 09

7.8 Parallel and Perpendicular
• Goals:
To identify parallel, perpendicular lines and
write an equation of a line containing a
point and parallel or perpendicular to a line
“parallel”
Slope and Line relationships
• Parallel lines have the same exact slope
(“m”) and a different y-intercept (“b”).
• y = 2x +3 and y = 2x +11 are parallel.
• All vertical lines are parallel.
x = -5 and x = 9 are parallel.
To determine if two equations are
parallel, change the equation to its slope
intercept form (y = mx + b)
Determine if the lines are parallel
y  3x  1 and y  3x  7
Y
Determine if the lines are parallel
Y
y  3x  1 and y  3x  7
3x
3x
y  3x  7
Determine if the lines are parallel
y  3x  1 and y  3x  1
N
y  3x  1
Must have different
y-intercept
N
5 y  x  2 and y  2  5 x
Determine if the lines are parallel
1
2
y  x
5
5
y  5x  2
Determine if the lines are parallel
1
x  4 and x 
3
All vertical
lines are
parallel.
Y
Determine if the lines are parallel
N
2 y  x  11 and y  2  2 x
1
11
y
x
2
2
y  2x  2
Determine if the lines are parallel
Y
3x  y  5 and 5 y  15 x  10
 y  3x  5 5 y  15 x  10
y  3x  5
y  3x  2
Determine if the lines are parallel
N
2 x  3 y  6 and y  7  3x
y  3x  7
3 y  2 x  6
2
6
y
x
3
3
y  3x  7
Determine if the lines are parallel
Y
2 x  4 y  3 and 3x  6 y  8
1
3
y  x
2
4
1
4
y  x
2
3
Perpendicular
means “at right angles”
All three red
lines are
perpendicular
to the green line.
8
4
3
B
E
2
1
-6
-4
-2
2
4
6
-1
A
-2
-3
4

Slope of AB is _______
7
-4
F
-5
-6
7
Slope of EF is _______

4
8
Slope and Line relationships
• Parallel lines have the same exact slope
(“m”) and a different y-intercept (“b”).
• y = 2x +3 and y = 2x +11 are parallel.
• Perpendicular lines (): have the
opposite reciprocal slopes
1
• y = 2x + 3 and y = - x  6
2
are perpendicular.
 2  1 
      1
 1  2 
Determine if the lines are perpendicular:
9
7
y  x  1 and y   x  7
7
9
Y
Determine if the lines are perpendicular:
7
8
y  x  4 and y  x  7
8
7
N
One must be positive;
the other negative.
Determine if the lines are perpendicular:
1
y  4 x  5 and y   x  3
4
Y
1
4
is the reciprocal of
4
1
Determine if the lines are perpendicular:
1
y  x  2 and y  5 x  3
5
Y
Determine if the lines are perpendicular:
y  2 and x  3
Y
Determine if the lines are perpendicular:
3 y  9 x  3 and 6 y  2 x  6
6 y  2 x  6
y  3x  1
Y
2
6
y
x
6
6
Write an equation of a line given a
point and perpendicular to the line
Given: (0,6) and y-3x =4
1.) Find slope: Solve for y, y=3x + 4
m= 3
2.) Take the Perpendicular to the slope
m=-1/3
3.) Use your m and your point and plug it into a new
y=mx+b
m=-1/3 (0,6) 6=-1/3 (0) + b
4.) solve for b, 6 =b
5.) write your equation with m and b y=-1/3x +6
Write an equation of the line containing the
given point and parallel to the line
(0,2) 3y-x =0
-
Solve for y to find the slope y=1/3 x
A slope parallel to m =1/3 would be m=1/3
Use your slope and ordered pair to solve for b
(0,2) m =1/3
2=1/3(0) +b
2=b and m=1/3
4. Write the equation with m and b
Y=1/3x +2
Assignment:
Page 340
(2-30) even
Show solving for “y”
3 Corners
•
•
•
•
•
Go to the:
1.) parallel,
2.) perpendicular
3.)neither corner
You may want a pencil and paper
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
y  3x  1 and y  3x  7
1
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
y  3x  1 and y  3x  7
1
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
3
y  3x  1 and y  3x  1
Must have different
y-intercept
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
3
5 y  x  2 and y  2  5 x
1
2
y  5x  2
y  x
5
5
Product of slopes
must be negative 1
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
1
x  4 and x 
3
All vertical lines are
parallel.
1
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
2
2 y  x  11 and y  2  2 x
1
11
y
x
2
2
y  2x  2
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
2
2 x  5 y  4 and 5 x  2 y  10
5 y  2 x  4 2 y  5 x  10
2
4
y
x
5
5
5
10
y
x
2
2
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
3
2 x  3 y  6 and y  7  3x
y  3x  7
3 y  2 x  6
2
6
y
x
3
3
y  3x  7
Determine if the lines are parallel (1),
perpendicular (2), or neither (3)
1
2 x  4 y  3 and 3x  6 y  8
1
3
y  x
2
4
1
4
y  x
2
3