for educational use only © 2010 5.2 defining slope brian preston algebra 1 2009-2010

For Educational Use Only © 2010

5.2 Defining Slope

Brian PrestonAlgebra 1 2009-

2010


How steep is this hiking trail?

Real World Application


Lesson Objectives

1) Find the slope of a line using two of its points.

2) Use the slope and any point on a line to write an equation of the line.


Review

1) 10 – ( – 7) = 17

2) – 3 – 4 = – 7

3) – 5 + 9 = 4


-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51xxxx

Review


DefinitionSlope –

range of the Y-value

range of the X-value

Slope –

m

Slope –

RiseRun


What is range?


range of the X-valueSlope –

Range – Highest number minus the Lowest number


PRESTON

P

Rise

Run

RiseRun

RiseRun

RiseRun

What does slope mean?


PRESTON

P

What does slope mean?


4) Yara & Nidal are hiking up a hill. The run for Yara’s step is 32 inches, and the rise is 8 inches. The run for Nidal’s step is 36 inches, and the rise is 9 inches. Find the slope of the lines representing each hikers pathway up the hill.

3232

of the Y-value

of the X-value

H-LH-L

range

range

8

936


=9 – 8

36 – 32=

1

4

slope

8

936


5) The coordinate plane below shows the position of a ladder resting against the side of a barn. Find the slope of the ladder.



5) The coordinate plane below shows the position of a ladder resting against the side of a barn. Find the slope of the ladder.


RiseRun

=– 6+2

– 3=


Definition

Slope –


range of the X-value

Slope –

m

Slope –

RiseRun

y2 – y1

x2 – x1

Slope –


6) Find the slope of the line containing the points P(– 2,4) & Q(5,– 6).

Example

– 6 – 4 5 – – 2

==y2 – y1

x2 – x1

– 10

7

– 2 4 – 65

( ) ( )

( )( )

(x1,y1) (x2,y2) 1 2


4 – – 6 ( )

6) Find the slope of the line containing the points P(– 2,4) & Q(5,– 6).

Example

– 2 – 5==y2 – y1

x2 – x1

10

– 7

– 2 4 – 65

( )( ) ( )

(x2,y2) (x1,y1) 2 1


7) Graph the line containing the point (– 2,3) and havingslope m = – 4

+3

– 4

+3

-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

Example

(– 2,3)

– 4

+3

Always make 3 points


-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

8) Graph the line containing the points (– 3,4) and (1,2).

Example

(– 3,4)(– 3,4)(1,2)

(1,2)


-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

9) Use the Coordinates of point R and Point S to find the slope of the horizontal line

shown below.

Example

0Rise

Run= =

Special line

R S

+5

ero

0 +5

0


-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

10) Use the Coordinates of Point J and Point K to find the slope of the vertical line

shown below.

Example

– 5

0

RiseRun

=

=Special line

J

K

– 5

u defined

0


– 3

2

– 3

2

Rise = – 3 Run = 2

11) Find the slope.

slope =

– 32

RiseRun

=

Example


x-int = 3 y-int = – 2

12) Find the slope.

slope =

3

2

2

3

RiseRun

=

-1

-3

-2

-4-5

-1-3 -2-4-5

1

2

3

4

5

2 3 4 51

– 2

Example

+2

+3

3


8 ÷ 0 =

Definition

Undefined means it doesn’t work, because we could put 0(nothing) in the cup infinite times and still not reach 8 oz.

undefined

nothing

nothing

nothing

nothing

nothing

noth

ing

noth

ing

noth

ing

noth

ing


u defined

Key Points & Don’t Forget

1) A negative times a negative is a positive. – 3 – 5 = 15

– 20

2) Slope =


pg. 231-232 #’s 11-19 odd,

20-42 even, 45, 47

The Assignment


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Bibliography

for educational use only © 2010 5.2 defining slope brian preston algebra 1 2009-2010

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