Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Sep 19­11:21 AM
Parallel lines
The lines on the graph are parallel lines.
What do you notice?
examples:
1. y = 2x + 6
2. y = 2x + 5
3. Y = 2x - 10
4. y = 2x
Oct 2­7:07 PM
1
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Parallel lines
They have the same slope (a)
What is different? The y intercept (b)
examples:
1. y = 2x + 6
2. y = 2x + 5
3. Y = 2x - 10
4. y = 2x
Oct 2­7:07 PM
Oct 13­11:31 AM
2
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Questions about parallel line...
Find the slope of a line that is parallel
­ the slopes are the same (a)
Then: find b using a point on the new line
Oct 13­10:01 AM
Example:
Find the equation of the line that is parallel to y=2x + 15 and passes through the point (6, 20)
Oct 13­10:03 AM
3
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Oct 13­11:47 AM
Perpendicular Lines
y = -2x - 2
y = ½x + 1
What do you notice?
Oct 2­7:08 PM
4
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Perpendicular Lines
y = -2x - 2
y = ½x + 1
The slope
One is positive and the other is negative
Both have "2"
Oct 2­7:08 PM
Perpendicular Lines
Lines that are perpendicular have
slopes that are a negative reciprocal
a becomes ­1/a
y= x+3
y = -4x -1
flip the fraction and change the sign
Oct 2­7:08 PM
5
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
When asked to find an equation of a line that is perpendicular
Determine the a of the first equation
Transform the a into its negative reciprocal (flip the fraction, change the sign) Then, using a point on the NEW line, calculate b
n.b. If the first fraction is an integer, it means the denominator is 1
2 = 2/1 and becomes ­1/2
Sep 19­12:00 PM
Change the slopes into a perpendicular slope
3
­4
1/5
2/3
5/6
­3/7
0 (y=5)
undefined (x=­4)
Oct 13­10:47 AM
6
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
y = -2 x + 6
y = -2 x - 2
y = 1/2x + 3
y = -2 x - 16
Oct 2­7:12 PM
Oct 2­7:21 PM
7
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Quiz on parallel perpendicular lines
Find the equation of the line of rue Heritage
(0,80)
e
ru
g
rita
(30, 85)
h
at
M
e e
H
e
u
r
(20, 40)
Oct 2­7:27 PM
Coincidental Lines:
Same Slope
Same y intercept (the same line)
Oct 13­10:49 AM
8
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
General Form
Sometimes we see an equation written like
this....
2x + 4y - 10 = 0
this is the general form
Ax + By + C = 0
Oct 2­7:22 PM
General Form
Ax + By + C = 0
A must be an integer
A must be positive
Oct 2­7:25 PM
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Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Often we try to put an equation
from general form to standard or
function form (y = ax + b)
In other words, we isolate y
General form to function form
2x + 4y - 10 = 0
4y = -2x + 10
y = -(2/4)x + 2.5
y = -½x + 2.5
Oct 2­7:23 PM
General Form to function form
put y to the other side (-y)
Make sure A is a positive integer
Examples
Oct 7­2:16 AM
10
Parallel and perpendicular lines notes oct 13.notebook
October 13, 2015
Oct 7­2:21 AM
Oct 5­1:57 AM
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