M. Pickens 2006

Slope

M. Pickens 2006

Objectives• To learn what slope is• To learn what a line looks like when it

has positive, negative, zero or undefined slope

• To learn how to find the slope of a graph

• To learn how to find the slope given 2 points

• To learn how to find the slope of a table

M. Pickens 2006

What is Slope?

Slope is the rate of change of a line

run

riseslope x

yslope

(change in y)

(change in x)

12

12

xx

yyslope

M. Pickens 2006

What does the line look like when…

• You have positive slope?

• You have negative slope?

• You have zero slope?

• You have NO slope?

M. Pickens 2006

Slope Mountain

Ski Resort

Positive slope, + work

Negative slope, - work

Zero slope is zero fun!

NO slope.

Oh No!!!!

T. Merrill 2005

M. Pickens 2006

Lets Cheer

Positive,Negative

ZeroNO

X-AxisY-Axis

Go, Go, Go

M. Pickens 2006

What Type of Slope is Shown?

Positive Slope

Negative Slope

Zero Slope

No Slope/Undefined

M. Pickens 2006

Slope of a Graph

• When slope is positive or negative we need to find the actual value of the slope or rate of change

• On a graph we find slope using the formula

run

riseslope

How far up or down it changes

How far left or right it changes

M. Pickens 2006

Slope of a Graph

1.First pick two points on the lineThe points need to be where the lines cross so they are integers

2. Then find the rise and run

3. Determine if the slope of the line is positive or negative

Rise = 2

Run = 3

run

riseslope

3

2

M. Pickens 2006

Slope of a Graph

1.First pick two points on the lineThe points need to be where the lines cross so they are integers

2. Then find the rise and run

3. Determine if the slope of the line is positive or negative

Rise = 10

Run = 2

run

riseslope

2

10 5

M. Pickens 2006

Slope of a Graphed Line

Find the slope of each line below

x

y

Slopes: RUN

RISE

1

1

4

4

4

4

Find the slope of each line below

06

0

1

4

2

8

4

3

undefined0

2

M. Pickens 2006

Slope of line through 2 points

• To find the slope of a line through 2 given points we use the formula

• For example, Find the slope of a line that goes through (-3, 5) and (2, 18)

12

12

xx

yyslope

X1 y1 X2 y2

12

12

xx

yyslope

185 2-3

5

13

M. Pickens 2006

Given two points on a line, find the slope:

1. (9, 2), (8, -7)

2. (-4, 4), (-7, 2)

3. (5, -1), (9, -4)

12

12

xx

yy

run

rise

98

27

1

9

12

12

xx

yy

47

42

59

14

3

2

47

42

59

14

4

3

X1 y1 X2 y2

9

X1y1 X2 y2

X1 y1 X2y2

3

2

M. Pickens 2006

Given two points on a line, find the slope:

4. (5, 2), (1, 0)

5. (3, -3), (3, -1)

6. (-4, -2), (4, -2)

12

12

xx

yy

run

rise

51

20

4

2

12

12

xx

yy

33

31

44

22

0

2

33

31 Undefined, NO slope

44

220

8

0

X1 y1 X2 y2

2

1

X1y1 X2 y2

X1 y1 X2y2

M. Pickens 2006

Slope of a Table• In a table we can use the same formula.

Pick any two pairs in the table for coordinates

x y

-4 -17

1 -2

3 4

8 19

10 25

Pick any two rows. If it is linear it will be the same

no matter which two rows you pick

12

12

xx

yyslope

x1x2

y1

y2 13

24

slope13

24

2

6 3

M. Pickens 2006

Slope of a Table

• Find the slope for each table below

x y

-3 4.25

-1 2.75

0 2

1 1.25

5 -1.75

x y

-8 2

-6 3

-3 4.5

-1 5.5

0 6

12

12

xx

yyslope

31

25.475.2

2

5.1

75.04

3

12

12

xx

yyslope

86

23

86

23

2

1

M. Pickens 2006

Slope of a Table

• Find the slope for each table below

x y

-10 17

-5 10

-1 4.4

5 -4

10 -11

x y

-3 -8

-1 -8

0 -8

1 -8

4 -8

12

12

xx

yyslope

105

1710

105

1710

5

7

12

12

xx

yyslope

31

88

31

88

2

0 0

M. Pickens 2006

Conclusion

• Slope is:

• Describe the slope of each of the following

the rate of change of a line

run

riseslope

12

12

xx

yyslope

Negative slope Undefined/ No slope

Positive slope Zero/0 slope