3-9 Parallel & Perpendicular Lines.notebook
October 28, 2015
3-9 Parallel & Perpendicular Lines
1
Parallel Lines:
Lines on a plane or graph that never intersect (cross).
Rules for Parallel Lines:
1) Have the same slope.
2) Have different y-intercepts.
Ex 1:
Are the lines y=-3x+4 and 6x+2y=-10 parallel lines?
Step1: Put both equations in y=mx+b form...
(solve for both for y).
y = -3x + 4
Y is already solved!
6x + 2y = -10
- 6x
- 6x
2y = -6x -10
2
2 2
y = -3x -5
y = -3x+4
y = -3x -5
Step2: Ask yourself two questions:
1) Do they have same slope?
2) Do they have different y-intercepts?
ANSWER
yes
yes
Yes, both lines are parallel
because both have same slope & different y-intercepts.
3-9 Parallel & Perpendicular Lines.notebook
3-9 Parallel & Perpendicular Lines
Checks for Example 1
October 28, 2015
3-9 Parallel & Perpendicular Lines.notebook
October 28, 2015
3-9 Parallel & Perpendicular Lines
Perpendicular Lines:
Lines that intersect to form a 90°angle.
Rule for Perpendicular
Parallel Lines: Lines:
1) Slope of one line is the negative
reciprocal of the slope of the other.
So, if line 1 has slope of +3, then line 2 must have a slope of
Reciprocal of +3?
1
3
+?
" "
Negative reciprocal of +3 =
Opposite of
1
3
1
3
3-9 Parallel & Perpendicular Lines.notebook
October 28, 2015
3-9 Parallel & Perpendicular Lines
Ex 2:
Determine if the graphs of 3y=9x+3 & 6y+2x=6 are perpendicular lines.
Step1: Put both equations in y=mx+b form...
(solve for both for y).
6y +2x = 6
- 2x - 2x
3y = 9x + 3
3 3 3
y = 3x + 1
6y = -2x + 6
6
6
y=
1
x
3
6
+1
one question:
1) Are the slopes of each line negative reciprocals?
y = 3x + 1
y=
ANSWER
1
3
x+1
because both slopes are negative reciprocals of each
other.
Checks for Example 2:
Determine whether the graphs of both lines are perpendicular.
1) 2y - x = 2
y = -2x + 4
2)
4y = 3x + 12
-3x + 4y -2 = 0
3)
ANSWER
Both lines
ARE perpendicular
ANSWER
Both lines
ARE NOT perpendicular
4y = -x + 12
4x = y - 2
ANSWER
Both lines
ARE perpendicular
3-9 Parallel & Perpendicular Lines.notebook
October 28, 2015
3-9 Parallel & Perpendicular Lines
Ex 3:
Write equation of a line (y=mx+b) containing point (-4,-3)
and perpendicular to line y=-4x-5.
Step1: Find negative reciprocal of slope for y=-4x-5
Slope =
-4
Negative
Reciprocal =
+1
New
Slope
4
Step2:
1 and plug into point slope-formula.
Use point (-4,-3) and slope
4
y - y1 = m(x - x1)
y
-3
1 x
4
-4
y - -3 =
1
4
(x - -4)
y + 3=
1
4
(x + 4)
y + 3=
1
4
x+(
1
4
)(4)
y + 3=
1
4
x+(
1
4
)(
Step 3: Solve for y:
y + 3=
1
4
x+(
4
4
y + 3=
1
4
x+1
y + 3=
-3
1
4
x+1
-3
4
1
)
ANSWER
Perpendicular to line y=-4x-5
)
3-9 Parallel & Perpendicular Lines.notebook
3-9 Parallel & Perpendicular Lines
Checks for Example 3:
October 28, 2015
6
3-9 Parallel & Perpendicular Lines.notebook
October 28, 2015
3-9 Parallel & Perpendicular Lines
7
Ex 4:
Step1: Find negative reciprocal of slope for
5
3
Slope =
Negative
Reciprocal =
+3
New
Slope
5
Step2:
3 and plug into point slope-formula.
Use point (-5,-2) and slope
5
y - y1 = m(x - x1)
y
-2
3 x
5
-5
y - -2 =
3
5
(x - -5)
y + 2=
3
5
(x + 5)
Step 3: Solve for y:
y + 2=
3
5
x+(
3
5
)(5)
y + 2=
3
5
x+(
3
5
)(
y + 2=
3
x
5
+ ( 15
)
5
y + 2=
3
5
x+3
y + 2=
-2
3
5
x+3
-2
ANSWER
Perpendicular to line
5
1
)
3-9 Parallel & Perpendicular Lines.notebook
3-9 Parallel & Perpendicular Lines
Checks for Example 4:
October 28, 2015
8