Slope Comes from the French verb monter Which means to climb or to rise.
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Transcript of Slope Comes from the French verb monter Which means to climb or to rise.
![Page 1: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/1.jpg)
![Page 2: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/2.jpg)
1 1( , )x y 2 2( , )x y
![Page 3: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/3.jpg)
1 1( , )x y 2 2( , )x y
Slope mComes from the French verb monter
Which means to climb or to rise
![Page 4: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/4.jpg)
1 1,x y
2 2,x y
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1 1,x y
2 2,x y
2 1,x y
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yChange in y
1 1,x y
2 2,x y
2 1,x y
2 1y y
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y
x
Change in y
Change in x
1 1,x y
2 2,x y
2 1,x y
2 1y y
2 1x x
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1 1( , )x y 2 2( , )x y
m yx
Change in y
Change in x
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1 1( , )x y 2 2( , )x y
2 1
2 1
y yx x
m y
x
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1 1( , )x y 2 2( , )x y
2 1
2 1
y yx x
m y
x
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2 1
2 1
y ymx x
![Page 12: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/12.jpg)
2 12 1 2
2 11
y ymx
x x xx
x
2 1 2 1x x m y y
1 22 1x xm y y
2 1 2 1y y m x x
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2 1 2 1y y m x x
1 1y y m x x
11Lets say we have one point,
And any of the infinite points on the line,
, ,
,
yP x
x y
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2 1 2 1y y m x x
1 1y y m x x
11Lets say we have one point,
And any of the infinite points on the line,
, ,
,
yP x
x y
![Page 15: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/15.jpg)
2 1 2 1y y m x x
1 1y y m x x
11Lets say we have one point,
And any of the infinite points on the line,
, ,
,
yP x
x y
![Page 16: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/16.jpg)
2 1
2 1
y ymx x
1 1y y m x x
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1 1y y m x x 1y 1y
1 1y m x x y
1 1y mx mx y
1 1y mx mx y
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1 1y mx mx y
1 1mxm yy x
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1 1y mx mx y
1 1mxm yy x
y bmx
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2 1
2 1
y ymx x
1 1y y m x x
y bmx
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Two nonvertical lines are PARALLEL if and only if
they have the same slope.
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59
y x
5 79
y x
5 79
y x
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59
y x
5 79
y x
5 79
y x
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59
y x
5 79
y x
5 79
y x
6:ZStandard
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59
y x
5 79
y x
5 79
y x
1y
15y 0,7, 79
x
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59
y x
5 79
y x
5 79
y x
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Two nonvertical lines are PERPENDICULAR if
and only if their slopes are negative
reciprocals
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5 29
y x
9 25
y x
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5 29
y x
9 25
y x
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5 29
y x
9 25
y x
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5 29
y x
9 25
y x
5:ZSquare
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Which of the following pairs of lines are parallel, perpendicular or neither?
2) 3 6 3 6x y and x y
13) 8 4 3 24x y and x y
1) 6 4 5 0.6 0.9 0.05x y and y x
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Which of the following pairs of lines are parallel, perpendicular or neither?
2) 3 6 3 6x y and x y
1) 6 4 5 0.6 0.9 0.05x y and y x
13) 8 4 3 24x y and x y
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
Weight on earth
x y
Weight on moon
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
140 1501301200
30
20
25
160
x y
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
140 1501301200
30
20
25
160
x y
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
x y
1) Determine The Slope
2) Determine a linear equation representing the weight y of a person on the moon as a function of his weight x on the earth
m =
y = mx + b
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
x y
1) Determine The Slope
2) Determine a linear equation representing the weight y of a person on the moon as a function of his weight x on the earth
m =
y = mx + b
16
16y x
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weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
x y
3) What is the weight of a man on the moon if his weight is 180 pounds on earth?
30 lbs
16
y x
8016
1y
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The temperature at which water freezes is
0o C or 32o F
The temperature at which water boils is
100o C or 212o F
Use this data to find a linear function that relates Celsius temperature to Fahrenheit temperature.
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Let the independent variable F stand for the Fahrenheit temperature
Freezes at 0o C or 32o F Boils at 100o C or 212o F
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Let the independent variable F stand for the Fahrenheit temperature
Let the dependent variable C stand for the Celsius temperature
1 1( , )x y 2 2( , )x y
1 1( , )F C 2 2( , )F C
Freezes at 0o C or 32o F Boils at 100o C or 212o F
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1 1( , )F C 2 2( , )F C
(?, ?)Freezes at 0o C or 32o F Boils at 100o C or 212o F
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1 1( , )F C 2 2( , )F C
(32,0) (?, ?)Freezes at 0o C or 32o F Boils at 100o C or 212o F
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)Freezes at 0o C or 32o F Boils at 100o C or 212o F
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)
2 1
2 1
C CmF F
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)
2 1
2 1FCm CF
100 0212 32
m
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)
100 0212 32
m
59
m
![Page 53: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/53.jpg)
1 1( , )F C 2 2( , )F C
(32,0) 212,100)59
m
1 159
C FC F
1 1y y m x x
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)59
m
1 159
C CC F
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)59
m
59
0 32C F
![Page 56: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/56.jpg)
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
![Page 57: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/57.jpg)
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
![Page 58: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/58.jpg)
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
Fahrenheit
Celcius
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1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
[0,225] x scale:25 by [0,100] y scale: 20
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Convert 78 degrees Fahrenheit to Celsius
78 degrees Fahrenheit is 25.6 Celsius
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78 degrees Fahrenheit is 25.6 Celsius
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5 329
C F
Give a verbal interpretation of the slope
59
m m yx
m CF
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5 329
C F
Give a verbal interpretation of the slope
59
m m yx
m CF
5 degrees change in Celsius9 degrees change in Fahrenheit
m
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5 degrees change in Celsius9 degrees change in Fahrenheit
m
![Page 65: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/65.jpg)
Give a verbal interpretation of the slope
5 degrees change in Celsius9 degrees change in Fahrenheit
m
There is a 5 degree change in the Celsius temperature.
For every 9 degree change in the Fahrenheit temperature.
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![Page 67: Slope Comes from the French verb monter Which means to climb or to rise.](https://reader036.fdocuments.net/reader036/viewer/2022062412/5a4d1adb7f8b9ab059974a97/html5/thumbnails/67.jpg)
Give a verbal interpretation of the slope
5 degrees change in Celsius9 degrees change in Fahrenheit
m
For every 5 degree change in the Celsius temperature.
There is a 9 degree change in the Fahrenheit temperature.