8/8/2019 Slope Algebra 23672
1/68
8/8/2019 Slope Algebra 23672
2/68
Find and use the slope of a line.
Graph parallel and perpendicular lines.
1) slope
2) rate of change
SlopeSlope
8/8/2019 Slope Algebra 23672
3/68
If the pilot doesnt change something, he / she will not make ithome for Christmas. Would you agree?
8/8/2019 Slope Algebra 23672
4/68
Consider the options:
1) Keep the same slope of his / her path.
8/8/2019 Slope Algebra 23672
5/68
Consider the options:
1) Keep the same slope of his / her path.
8/8/2019 Slope Algebra 23672
6/68
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
8/8/2019 Slope Algebra 23672
7/68
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.
8/8/2019 Slope Algebra 23672
8/68
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.
8/8/2019 Slope Algebra 23672
9/68
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.Not possible! This is an airplane, not a helicopter.
8/8/2019 Slope Algebra 23672
10/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
8/8/2019 Slope Algebra 23672
11/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
8/8/2019 Slope Algebra 23672
12/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
8/8/2019 Slope Algebra 23672
13/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
vertical changehorizontal change
ySlope
x
(! !
(
8/8/2019 Slope Algebra 23672
14/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
vertical changehorizontal change
ySlope
x
(! !
(
8/8/2019 Slope Algebra 23672
15/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
vertical changehorizontal change
ySlope
x
(! !
(
8/8/2019 Slope Algebra 23672
16/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
vertical changehorizontal change
ySlope
x
(! !
(
8/8/2019 Slope Algebra 23672
17/68
F ortunately, there is a way to measure a proper slope to clear the obstacle.
We measure the change in height requiredand divide that by the horizontal change required.
y(
x(
vertical changehorizontal change
ySlope
x
(! !
(
8/8/2019 Slope Algebra 23672
18/68
vertical change 4,000 4 2horizontal change 10,000 10 5
y ft Slope
x ft
(! ! ! ! !
(
y
x10000
10000
00
y(
x(
8/8/2019 Slope Algebra 23672
19/68
x
y
FINDING THE SLOPE O F A LIN E
SlopeSlope
8/8/2019 Slope Algebra 23672
20/68
x
y
FINDING THE SLOPE O F A LIN E
The slope m of the non-vertical linepassing through the pointsand is
1 1( , ) x y
2 2( , ) x y
1 1( , ) x y
2 2( , ) x y
SlopeSlope
8/8/2019 Slope Algebra 23672
21/68
x
y
FINDING THE SLOPE O F A LIN E
rise
runm !
The slope m of the non-vertical linepassing through the pointsand is
1 1( , ) x y
2 2( , ) x y
1 1( , ) x y
2 2( , ) x y
SlopeSlope
8/8/2019 Slope Algebra 23672
22/68
x
y
FINDING THE SLOPE O F A LIN E
rise
runm !
The slope m of the non-vertical linepassing through the pointsand is
1 1( , ) x y
2 2( , ) x y
1 1( , ) x y
2 2( , ) x y
ychange inchange xin
!
SlopeSlope
8/8/2019 Slope Algebra 23672
23/68
x
y
2 1 x x
FINDING THE SLOPE O F A LIN E
rise
runm !
The slope m of the non-vertical linepassing through the pointsand is
1 1( , ) x y
2 2( , ) x y
1 1( , ) x y
2 2( , ) x y
2 1 y yychange inchange xin
! 2 1
2 1 x x y y
!
SlopeSlope
8/8/2019 Slope Algebra 23672
24/68
8/8/2019 Slope Algebra 23672
25/68
y
x
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
(1, 1)
(3, 6)
SlopeSlope
8/8/2019 Slope Algebra 23672
26/68
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)slope = =
ris e ym run x
(
! (
SlopeSlope
8/8/2019 Slope Algebra 23672
27/68
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)slope = =
ris e ym run x
(
! (
SlopeSlope
8/8/2019 Slope Algebra 23672
28/68
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
rise = 6 - 1= 5 units
slope = =ris e y
m run x
(
! (
SlopeSlope
8/8/2019 Slope Algebra 23672
29/68
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
run = 3 - 1= 2 units
rise = 6 - 1= 5 units
slope = =ris e y
m run x
(
! (
SlopeSlope
8/8/2019 Slope Algebra 23672
30/68
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
run = 3 - 1= 2 units
rise = 6 - 1= 5 units
slope = =ris e y
m run x
(
! (
5= 2
SlopeSlope
8/8/2019 Slope Algebra 23672
31/68
y
x
SlopeSlope
F ind the slope of the line.
(2, 3)
(8, 8)
8/8/2019 Slope Algebra 23672
32/68
y
x
SlopeSlope
F ind the slope of the line.
(2, 3)
(8, 8)
riseslope =
run
8/8/2019 Slope Algebra 23672
33/68
y
x
SlopeSlope
F ind the slope of the line.
(2, 3)
(8, 8)
run = 8 - 2= 6 units
rise = 8 - 3= 5 units
riseslope =
run
8/8/2019 Slope Algebra 23672
34/68
y
x
SlopeSlope
F ind the slope of the line.
(2, 3)
(8, 8)
run = 8 - 2= 6 units
rise = 8 - 3= 5 units
riseslope =
run5
=6
8/8/2019 Slope Algebra 23672
35/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
SlopeSlope
8/8/2019 Slope Algebra 23672
36/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
37/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
38/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
2 1
2 1 x y
my
x!
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
39/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
2 1
2 1 x y
my
x!
4 (1
)74
!
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
40/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
-8
8
2 1
2 1 x y
my
x!
4 (1
)74
!
88
!
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
41/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
-8
8
2 1
2 1 x y
my
x!
4 (1
)74
!
88
!
1!
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
42/68
P lot the points (-4, 7) and (4, -1) and draw a line through them.F ind the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4, 7) P x y ! 2 2 2( , ) (4, 1) P x y !
-8
8
2 1
2 1 x y
my
x!
4 (1
)74
!
88
!
1!
Negative slope:F alls from left to right
1 ( 4,7) P
2 (4, 1) P
SlopeSlope
8/8/2019 Slope Algebra 23672
43/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
SlopeSlope
8/8/2019 Slope Algebra 23672
44/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
SlopeSlope
8/8/2019 Slope Algebra 23672
45/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) F ollow the slope of to locate another point on the line. 1
2
SlopeSlope
8/8/2019 Slope Algebra 23672
46/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) F ollow the slope of to locate another point on the line. 1
2
SlopeSlope
8/8/2019 Slope Algebra 23672
47/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) F ollow the slope of to locate another point on the line. 1
2
SlopeSlope
8/8/2019 Slope Algebra 23672
48/68
8/8/2019 Slope Algebra 23672
49/68
8/8/2019 Slope Algebra 23672
50/68
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) F ollow the slope of to locate another point on the line. 1
2
3) Draw the line, connecting the two points.
SlopeSlope
8/8/2019 Slope Algebra 23672
51/68
y
x
If the line rises to the right,then the slope is positive.
SlopeSlope
ll
8/8/2019 Slope Algebra 23672
52/68
y
x
If the line rises to the right,then the slope is positive.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
53/68
y
x
If the line rises to the right,then the slope is positive.
y
x
If the line falls to the right,then the slope is negative.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
54/68
y
x
If the line rises to the right,then the slope is positive.
y
x
If the line falls to the right,then the slope is negative.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
55/68
y
x
If the line is horizontal,then the slope is zero.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
56/68
y
x
If the line is horizontal,then the slope is zero.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
57/68
y
x
If the line is horizontal,then the slope is zero.
y
x
If the line is vertical,then the slope isundefined.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
58/68
y
x
If the line is horizontal,then the slope is zero.
y
x
If the line is vertical,then the slope isundefined.
SlopeSlope
SlSl
8/8/2019 Slope Algebra 23672
59/68
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel .
SlopeSlope
8/8/2019 Slope Algebra 23672
60/68
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel .w ith the same slope
SlopeSlope
8/8/2019 Slope Algebra 23672
61/68
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel .w ith the same slope
8/8/2019 Slope Algebra 23672
62/68
SlopeSlope
8/8/2019 Slope Algebra 23672
63/68
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.
SlopeSlope
SlopeSlope
8/8/2019 Slope Algebra 23672
64/68
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
SlopeSlope
SlopeSlope
8/8/2019 Slope Algebra 23672
65/68
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
SlopeSlope
SlopeSlope
8/8/2019 Slope Algebra 23672
66/68
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
SlopeSlope
SlopeSlope
8/8/2019 Slope Algebra 23672
67/68
SlopeSlope
CreditsCredits
8/8/2019 Slope Algebra 23672
68/68
CreditsCredits
P ower P ointcreated by
Using Glencoes Algebra 2 text, 2005
http://robertfant.com
Top Related