6.6 Warm-up
description
Transcript of 6.6 Warm-up
![Page 1: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/1.jpg)
![Page 2: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/2.jpg)
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
![Page 3: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/3.jpg)
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
![Page 4: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/4.jpg)
Pardekooper
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
![Page 5: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/5.jpg)
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
![Page 6: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/6.jpg)
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.
![Page 7: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/7.jpg)
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.
![Page 8: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/8.jpg)
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
![Page 9: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/9.jpg)
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
![Page 10: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/10.jpg)
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?
![Page 11: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/11.jpg)
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?
![Page 12: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/12.jpg)
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.
![Page 13: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/13.jpg)
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.
![Page 14: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/14.jpg)
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.
![Page 15: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/15.jpg)
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.
![Page 16: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/16.jpg)
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.
![Page 17: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/17.jpg)
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 ?
![Page 18: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/18.jpg)
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 ?
![Page 19: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/19.jpg)
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 ?
![Page 20: 6.6 Warm-up](https://reader035.fdocuments.us/reader035/viewer/2022062309/56813cc1550346895da66cac/html5/thumbnails/20.jpg)
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