03.03 skm & pp 1 slope. 03.03 skm & pp 2 definition: slope the slope of the line containing...

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03.03 S KM & PP 1 Slope

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Page 1: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 1

Slope

Page 2: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

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.

Page 3: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

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

Page 4: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 4

m

Slope

xy

21

12

12 xx,xxyy

m

xinchange

yinchange

RunRise

xdelta

ydelta

Page 5: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 5

Compute the Slope

(-2, -3)

(4, -1)

3

1

6

2

24

31

)(

m

upwards

Page 6: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 6

Another Slope

(-4, -3)

(0, 5)

21

2

4

8

40

35

m

upw

ards

Page 7: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 7

Compute this Slope

(-5, 2)

(4, -1)

3

1

9

3

54

21

)(

m

DOWNWARDS

Page 8: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 8

Compute the Slope

(-5, -1)

(4, -1)

0

9

0

54

11

)(

m

HORIZONTAL

Page 9: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 9

Compute the Slope

(-4, -5)

(-4, 0)

Undefined

)(m

0

5

44

50

VER

TIC

AL

Page 10: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 10

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)

Page 11: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 11

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.

Page 12: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

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

Page 13: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

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.

Page 14: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

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.

Page 15: 03.03 SKM & PP 1 Slope. 03.03 SKM & PP 2 Definition: Slope The slope of the line containing points P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) is given by The

03.03 S KM & PP 15

That’s All for Now!