M. Pickens 2006

Slope

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

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 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