Algebra Lesson 6-1

Created by Jeff M. Downs

Important Vocabulary Terms

The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line.

You can describe steepness by using slope of a line.

The Slope Ratio

horizontal run = 5

vertical rise = 10

slope =vertical rise

horizontal run

so

slope = 105

= 21

= 2

Remember to always simplify the ratio.

Let’s Try It Out!

horizontal run = 200 ft

vertical rise = 40 ft

Let’s try and find the slope of a hill that has a vertical rise of 40ft and a horizontal run of 200ft. Let m represent the slope.

Don’t touch that button unless you have tried it on your own first!

SClick the green solution button to check your own work

Apply the formula- vertical rise to horizontal run

Vertical rise = 40 ft

Horizontal run = 200 ft

40 ft.200 ft.

40

Find the GCF

= 1 5

The slope of the hill is1 5

back forward

1

3

5

7

y

-1-1 1 3 5 7

..

USING A COORDINATE PLANE TO FIND SLOPE

The coordinates are (2,2) and (6,5)

Use the formula:

rise run

= 5 - 2 6 - 2 =

3 4

..

(x2, y2)

(x1, y1)x2 - x1

y2 - y1

The slope m of a line that passes through the points (x1, y1) and (x2, y2) is

m =riserun =

change in y change in x =

y2 - y1

x2 - x1

The Slope Of A Line

1. Positive Slope

2. Negative Slope

3. Zero Slope

4. Undefined Slope

A line that rises from left to right

A line falls from left to right

A line is horizontal

The line is vertical

*Continue to click mouse for information*

It’s your turn:

Use a piece of graph paper to help you illustrate the slope

(x , y )1 1 = (1,0) and (x , y ) = (3, 4)

2 2

(x , y )1 1 = (0, 9) and (x , y ) = (4, 7)

2 2

(x , y )1 1 = (1, 2) and (x , y ) = (5, 2)

2 2

1

3

5

7

y

-1-1 1 3 5 7.

(x , y )1 1 = (1, 0) and (x , y ) = (3, 4)

2 2

m = y

2 y

1-

x 2

x 1-

m = 4 - 03 - 1

m = 42

.

The slope of the line is 2

1

3

5

7

y

-1-1 1 3 5 7

. m =

y2

y1-

x 2

x 1-

m = 7 - 94 - 0

.(x , y )

1 1 = (0, 9) and (x , y ) = (4, 7)2 2

The slope of the line is -1 which makes it a negative slope. 2

m = -2 4

or-1 2

(x , y )1 1 = (1, 2) and (x , y ) = (5, 2)

2 2

1

3

5

7

y

-1-1 1 3 5 7

m = y

2 y

1-

x 2

x 1-

m = 2 - 25 - 1

The slope of the line is zero which makes it a zero slope.

m = 0 4

or 0

. .

Let’s Review

• Slope is the steepness of a line

• It is described by a ratio of rise to run

• A coordinate plane can be used to find the slope of a line

• There are 4 types of slope– positive slope

– negative slope

– zero slope

– undefined slope