Dr. Fowler CCM

Slope - Easier

x

yslope

Slope can be expressed different ways:

A line has a positive slope if it isgoing uphill from left to right.

A line has a negative slope if it isgoing downhill from left to right.

What is Slope?Slope is the rate of change of a line

change in y

change in x2 1

2 1

( ) vertical change

( ) horizontal change

y y risem

x x run

We use the letter m becausethe French word for “to go up” is monter.

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

No Notes Needed – Just Watch

Start with the lower point and count how much you rise and run to get to the other point!

Determine the slope of the line.

6

3

run

3

6= =

1

2

rise

Notice the slope is positive AND the line increases!

Second Way – Pick 2 points on the graph (-2, -2) and (4, 1).

(1 ( 2))

(4 ( 2))m

2 1

2 1

( )

( )

y ym

x x

(1 2)

(4 2)

Use the formula!

y2 is the 2nd y… (y2 = 1)

y1 is the 1st y… (y1 = -2)

13

6 2

Notice you get the same answer either way. Which do you think is easiest? Rise/Run or pick 2 points?

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. Volunteer for first?

06

0

1

4

2

8

4

3

undefined0

2

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

47

42

59

14

3

2

47

42

59

14

4

3

X1y1 X2

y2

9

3

2

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

33

31

44

22

0

2

33

31 UndefinedNO slope

44

220

8

0

X1y1 X2

y2

2

1

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

x1

x2

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

-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

y = mx + b.

m = slope

b = y-intercept

Given an equation of a line, find theslope and y-intercept.

Example: Find the slope and y-intercept:

1) y = 3x + ½ slope= 3 y-intercept = ½

The End

Excellent Job !!!Well Done

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