slope comes 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

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.