The graph of which function is shown ?
y
30
a. Y = 30x
b. Y = 30 - x
20
c. Y = 30 - (x+5)
d. y = 30 - 5x
10
0
0
2
4
6
x
Pardekooper
The graph of which function is shown ?
y
30
a. Y = 30x
b. Y = 30 - x
20
c. Y = 30 - (x+5)
d. y = 30 - 5x
10
0
0
2
4
6
x
Pardekooper
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Pardekooper
What you’ll learn
To determine if two lines are parallel or
perpendicular by their slopes, and
To write equations of lines that pass
through a given point, parallel or
perpendicular to the graph of the given
equation
Pardekooper
Here are some terms.
Two lines are parallel if and only if they
have the same slope.
y  4x  5
example:
y  4x  8
Two lines are perpendicular if and only if
their slopes are opposite inverses.


example:
2
y  x 5
3
3
y
x2
2

Pardekooper
Lets try some.
Is the following set of
lines parallel or
perpendicular?
y=2x+3
y=2x-5
parallel
Pardekooper
Lets try some.
Is the following set of
lines parallel or
perpendicular?
y=1/2x+3
y= -2x-5
perpendicular
Pardekooper
Lets try some.
Is the following set of
lines parallel or
perpendicular?
1
y= /4x+1
y=4x-1
neither
Pardekooper
Where do the equations
come from?
Write the equation for the
that is parallel to y=5x-1
with y-intercept of 2.
m=5
b=2
y=mx+b
y=5x+2
Pardekooper
Where do the equations
come from?
Write the equation for the
that is parallel to y=2/3x-1
with y-intercept of -1.
2
m= /3
b=-1
y=mx+b
y=2/3x-1
Pardekooper
Where do the equations
come from?
Write the equation for the
that is perpendicular to
y=2/3x-1 with y-intercept of -4.
-3
m= /2
b=-4
y=mx+b
y=-3/2x-4
Pardekooper
Where do the equations
come from?
Write the equation for the that
is perpendicular to y=-1/4x-1
with y-intercept of 5.
4
m= /1
b=5
y=mx+b
y=4x+5
Pardekooper
Where do the equations
come from?
Write an equation for a line
that passes through the point
(1,3)and is parallel to y=2x+4.
m=2
P(1,3)
y-y1=m(x-x1)
y-3=2(x-1)
Pardekooper
Where do the equations
come from?
Write an equation for a line
that passes through the point
(2,-4)and is parallel to
y=2/3x+4.
2
m= /3
P(2,-4)
y-y1=m(x-x1)
y-(-4)=2/3(x-2)
Pardekooper
Where do the equations
come from?
Write an equation for a line
that passes through the point
(1,-3)and is perpendicular to
y=2/3x+1.
-3
m= /2
P(1,-3)
y-y1=m(x-x1)
y-(-3)=-3/2(x-1)
Pardekooper
Why do we need to know if lines
are parallel or perpendicular ?
Given a pair of opposite
sides of a quadrilateral are
parallel, what does the
quadrilateral look like ?
Pardekooper
Why do we need to know if lines
are parallel or perpendicular ?
Given a pair of opposite
Given
pair of opposite
sides
of aa quadrilateral
are
sides
of
a
quadrilateral
are
parallel and equal in
parallel,
what
does
the
length,what does the
quadrilateral look
look like
like ??
quadrilateral
In order to know which one, you
need more information.
Pardekooper
Why do we need to know if lines
are parallel or perpendicular ?
Givenaapair
pairof
ofopposite
opposite
Given
sidesof
ofaaquadrilateral
quadrilateralare
are
sides
parallel
andand
equal
in length,
parallel
equal
in
andlength,what
a pair of adjacent
does thesides
form
a right angle,what
quadrilateral
look like does
?
the quadrilateral look like ?
We need some more information.
Pardekooper
3.7 Slopes of Parallel and Perpendicular Lines
Geometry
Are the lines parallel, perpendicular or neither
1. y = -5x
2. y=3x+1
y = 5x - 18
y=-1/3x+4
3. y=1/2x-4
y=1/2x+4
Write an equation for a line that passes through the point and is parallel to the given equation.
4. (2,-7), y = x - 2
5. (1,-2), y = -2x + 7
6. (2,-1), y = -0.5x + 2
Write an equation for a line that passes through the point and is perpendicular to the given equation.
7. (6,-2), y = 3/5x - 4
8. (3,7), y = 3/4x -1
9. Write an equation of the line that has an y-intercept of 3 and is perpendicular to the graph of
5x - 3y = 2.
10. Use slope to show that opposite sides of hexagon RSTUVW are parallel.
R
S
T
W
V
U
11. Use slope to determine whether a triangle with vertices G(3,2), H(8,5), and K(0,10) is a right triangle.