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1 1( , )x y 2 2( , )x y
1 1( , )x y 2 2( , )x y
Slope mComes from the French verb monter
Which means to climb or to rise
1 1,x y
2 2,x y
1 1,x y
2 2,x y
2 1,x y
yChange in y
1 1,x y
2 2,x y
2 1,x y
2 1y y
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
1 1( , )x y 2 2( , )x y
m yx
Change in y
Change in x
1 1( , )x y 2 2( , )x y
2 1
2 1
y yx x
m y
x
1 1( , )x y 2 2( , )x y
2 1
2 1
y yx x
m y
x
2 1
2 1
y ymx x
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
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
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
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
2 1
2 1
y ymx x
1 1y y m x x
1 1y y m x x 1y 1y
1 1y m x x y
1 1y mx mx y
1 1y mx mx y
1 1y mx mx y
1 1mxm yy x
1 1y mx mx y
1 1mxm yy x
y bmx
2 1
2 1
y ymx x
1 1y y m x x
y bmx
Two nonvertical lines are PARALLEL if and only if
they have the same slope.
59
y x
5 79
y x
5 79
y x
59
y x
5 79
y x
5 79
y x
59
y x
5 79
y x
5 79
y x
6:ZStandard
59
y x
5 79
y x
5 79
y x
1y
15y 0,7, 79
x
59
y x
5 79
y x
5 79
y x
Two nonvertical lines are PERPENDICULAR if
and only if their slopes are negative
reciprocals
5 29
y x
9 25
y x
5 29
y x
9 25
y x
5 29
y x
9 25
y x
5 29
y x
9 25
y x
5:ZSquare
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
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
weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
Weight on earth
x y
Weight on moon
weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
140 1501301200
30
20
25
160
x y
weight on earth (lb)
weight on moon (lb)
120 20
132 22
156 26
162 27
140 1501301200
30
20
25
160
x y
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
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
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
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.
Let the independent variable F stand for the Fahrenheit temperature
Freezes at 0o C or 32o F Boils at 100o C or 212o F
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
1 1( , )F C 2 2( , )F C
(?, ?)Freezes at 0o C or 32o F Boils at 100o C or 212o F
1 1( , )F C 2 2( , )F C
(32,0) (?, ?)Freezes at 0o C or 32o F Boils at 100o C or 212o F
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
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
2 1
2 1
C CmF F
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
2 1
2 1FCm CF
100 0212 32
m
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
100 0212 32
m
59
m
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
1 1( , )F C 2 2( , )F C
(32,0) 212,100)59
m
1 159
C CC F
1 1( , )F C 2 2( , )F C
(32,0) 212,100)59
m
59
0 32C F
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
1 1( , )F C 2 2( , )F C
(32,0) 212,100)
5 329
C F
Fahrenheit
Celcius
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
Convert 78 degrees Fahrenheit to Celsius
78 degrees Fahrenheit is 25.6 Celsius
78 degrees Fahrenheit is 25.6 Celsius
5 329
C F
Give a verbal interpretation of the slope
59
m m yx
m CF
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
5 degrees change in Celsius9 degrees change in Fahrenheit
m
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.
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.