03.03 S KM & PP 1

Slope

03.03 S KM & PP 2

Definition: Slope

The slope of the linecontaining points

P1(x1, y1) and P2(x2, y2) is given by

21

12

12 xx,xxyy

m

The denominator

can’t be zero.

03.03 S KM & PP 3

A Slope Triangle

21

12

12 xx,xxyy

m

P1(x1, y1)

RUNx2 - x1

RISEy2 - y1

P2(x2, y2)

RISEy2 - y1

x2 - x1

RUN

03.03 S KM & PP 4

m

Slope

xy

21

12

12 xx,xxyy

m

xinchange

yinchange

RunRise

xdelta

ydelta

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Compute the Slope

(-2, -3)

(4, -1)

3

1

6

2

24

31

)(

m

upwards

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Another Slope

(-4, -3)

(0, 5)

21

2

4

8

40

35

m

upw

ards

03.03 S KM & PP 7

Compute this Slope

(-5, 2)

(4, -1)

3

1

9

3

54

21

)(

m

DOWNWARDS

03.03 S KM & PP 8

Compute the Slope

(-5, -1)

(4, -1)

0

9

0

54

11

)(

m

HORIZONTAL

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Compute the Slope

(-4, -5)

(-4, 0)

Undefined

)(m

0

5

44

50

VER

TIC

AL

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SLOPEBASICS

POSITIVE SLOPE The line rises from left to right.

ZERO SLOPE The line is HORIZONTAL (zero rise)

NEGATIVE SLOPEThe line falls from left to right.

UNDEFINED SLOPEThe line is VERTICAL (zero run)

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Practice Problem 1a

3

2

Determine the slope of the line

containing points P1 and P2. ),(P 571 ),(P 912

6

4

71

59

)(

m

RUN = 3

RISE = 2

The line rises from left to right.

03.03 S KM & PP 12

Practice Problem 1b

Determine the slope of the line

containing points P1 and P2. ),(P 531 ),(P 232

0

7

33

52

)(

m

The slope is undefined.

Vertical Line

03.03 S KM & PP 13

Practice Problem 1c

2

1

Determine the slope of the line

containing points P1 and P2. ),(P 301 ),(P 542

4

2

04

35

)(

m

RUN = 2

RISE = -1

The line falls from left to right.

03.03 S KM & PP 14

Practice Problem 1d

0

Determine the slope of the line

containing points P1 and P2. ),(P 571 ),(P 512

6

0

71

55

)(

m

RUN = 6RISE = 0

The line is Horizontal.

03.03 S KM & PP 15

That’s All for Now!