pardekooper the graph of which function is shown ? a. y = 30x b. y = 30 - x c. y = 30 - (x+5) d. y =...
TRANSCRIPT
PardekooperPardekooper
The graph of which function is shown ?
a. Y = 30xb. Y = 30 - xc. Y = 30 - (x+5)
d. y = 30 - 5x
0 2 4 6
0
10
20
30y
x
PardekooperPardekooper
0 2 4 6
0
10
20
30y
x
The graph of which function is shown ?
a. Y = 30xb. Y = 30 - xc. Y = 30 - (x+5)
d. y = 30 - 5x
Pardekooper
QuickTime™ and aTIFF (Uncompressed) decompressor
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What you’ll learnTo 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
PardekooperPardekooper
Two lines are Two lines are parallelparallel if if and only if they have the and only if they have the same slope.same slope.example:
example:
€
y = 4x + 5
€
y = 4x + 8
€
y =2
3x −5
€
y =−3
2x + 2
PardekooperPardekooper
Two lines are Two lines are perpendicularperpendicular if and only if their slopes if and only if their slopes are opposite inverses.are opposite inverses.
Here are some terms.
Is the following Is the following set of lines set of lines parallel or parallel or
perpendicular?perpendicular?y=2x+3y=2x-5
PardekooperPardekooper
parallel
Lets try some.
Is the following Is the following set of lines set of lines parallel or parallel or
perpendicular?perpendicular?
PardekooperPardekooper
Lets try some.
y=1/2x+3y= -2x-5
perpendicular
Is the following Is the following set of lines set of lines parallel or parallel or
perpendicular?perpendicular?
PardekooperPardekooper
Lets try some.
y=1/4x+1y=4x-1
neither
Write the equation Write the equation for the that is for the that is
parallel to y=5x-1 parallel to y=5x-1 with y-intercept of with y-intercept of
2.2.
m=5
PardekooperPardekooper
b=2
y=mx+by=5x+2
Where do the equations come
from?
Write the equation Write the equation for the that is for the that is
parallel to y=parallel to y=22//33x-1 x-1 with y-intercept of with y-intercept of
-1.-1.m=2/3
PardekooperPardekooper
b=-1
y=mx+by=2/3x-1
Where do the equations come
from?
m=-3/2
PardekooperPardekooper
b=-4
y=mx+by=-3/2x-4
Where do the equations come
from?Write the equation Write the equation for the that is for the that is perpendicular to perpendicular to y=y=22//33x-1 with y-x-1 with y-intercept of -4.intercept of -4.
m=4/1
PardekooperPardekooper
b=5
y=mx+by=4x+5
Where do the equations come
from?Write the equation for Write the equation for the that is the that is
perpendicular to y=perpendicular to y=--
11//44x-1 with y-x-1 with y-intercept of 5.intercept of 5.
m=2
PardekooperPardekooper
P(1,3)
y-y1=m(x-x1)y-3=2(x-1)
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=2/3
PardekooperPardekooper
P(2,-4)
y-y1=m(x-x1)y-(-4)=2/3(x-2)
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.
m=-3/2
PardekooperPardekooper
P(1,-3)
y-y1=m(x-x1)y-(-3)=-
3/2(x-1)
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.
PardekooperPardekooper
Why do we need to know if lines are parallel or
perpendicular ?Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are
parallel, what does parallel, what does the quadrilateral the quadrilateral
look like ?look like ?
PardekooperPardekooper
Why do we need to know if lines are parallel or
perpendicular ?Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are
parallel, what does parallel, what does the quadrilateral the quadrilateral
look like ?look like ?In order to know which one, you need more
information.
Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length,what does ,what does the quadrilateral the quadrilateral
look like ?look like ?
Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length,what does ,what does the quadrilateral the quadrilateral
look like ?look like ?
PardekooperPardekooper
Why do we need to know if lines are parallel or
perpendicular ?
We need some more information.
Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length, and a , and a pair of adjacent pair of adjacent
sides form a right sides form a right angleangle,what does the ,what does the quadrilateral look quadrilateral look
like ?like ?
Geometry
Are the lines parallel, perpendicular or neither1. y = -5x 2. y=3x+1 3. y=1/2x-4 y = 5x - 18 y=-1/3x+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.
11. Use slope to determine whether a triangle with vertices G(3,2), H(8,5), and K(0,10) is a right triangle.
3.7 Slopes of Parallel and Perpendicular Lines3.7 Slopes of Parallel and Perpendicular Lines
W
R S
T
UV