Slope

By Lia Servidio and Kelly Lively

What is Slope?

Slope is a measure of how steep a line isThe greater the slope value, the steeper

the line

Slope Formula

Slope is generally represented as the letter m

Equal to the change in the y-coordinates divided by the change in the x-coordinates

x

y

run

risem

How to Find Slope From Two Points

1. Identify the two points: (x1,y1) and (x2,y2)

2. Use the formula m=(y2-y1)/(x2-x1)

*It does not matter which set of coordinates are considered to be (x1,y1) and which are considered to be (x2,y2)

Example

What is the slope between the points (-2,5) and (6,10)?

If (x1,y1)=(-2,5) and (x2,y2)=(6,10)

8

5

))2(6(

)510(

)(

)(

12

12

m

m

xx

yym

x

ym

If (x1,y1)=(6,10) and (x2,y2)=(-2,5)

8

5

8

5

)6)2((

)105(

)(

)(

12

12

m

m

xx

yym

x

ym

How to Find Slope From an Equation

*Slope is equal to m in the equation y=mx+b

Set the equation equal to y (if not already) Slope is equal to the constant in front of x

Examples

What is the slope of the line y=4x+7?

1. Since the equation is already set equal to y, look for the constant next to the x.

2. y=4x+7, m=4

What is the slope of the line 6x+3y=12?

3. Set the equation equal to y: 3y=-6x+12

y=-2x+4

2. Look for the constant next to the x, m=-2

How to Find Slope Using a Graph

Horizontal and Vertical Lines

The slope of a horizontal line is 0 because there is no change in y

The slope of a vertical line is undefined because it is impossible to divide by 0 and there is no change in x

00

xx

y

run

risem

undefinedy

x

y

run

risem

0

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Welcome to

Who Wants to be a Millionaire

50:50

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Another

Presentation

© 2002 - All rights Reservednygiantsbigblue@yahoo.com

© Mark E. Damon - All Rights Reserved

© Mark E. Damon - All Rights Reserved

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: -11/2

C: -1

B: 11/2

D: 2/11

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope of the line through the pair of points:

(-4,7),(-6,-4)

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 5/7

C: -7

B: 5

D: -5

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope:

y=-5x-7

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151413121110987654321

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© Mark E. Damon - All Rights Reserved

A: 0

C: -1

B: 1

D: Undefined

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope of the line through the pair of points:

(19,3),(2,3)

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 2/3

C: - 1/2

B: 3/2

D: 2

50:50

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$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope:

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 0

C: Undefined

B: 1

D: -1

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope of the line through the pair of points:

(17,-13),(17,8)

© Mark E. Damon - All Rights Reserved

Congratulations!

You’ve ReachedYou’ve Reached

the $1,000the $1,000

Milestone!Milestone!

Congratulations!Congratulations!

© Mark E. Damon - All Rights Reserved

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 9/8

C: 3/8

B: -8/3

D: -1/3

50:50

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$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope:

8x+3y=-9

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 3/2

C: 1

B: Undefined

D: 0

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

What is the

slope of this line?

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$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: Undefined

C: 1

B: 0

D: -1

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope:

x=-1

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: k

C: m

B: x

D: y

50:50

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$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

What letter is commonly used to represent slope?

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© Mark E. Damon - All Rights Reserved

A: Rise/Run

C: ΔY/ ΔX

B: (y2-y1)/(x2-x1)

D: Run/Rise

50:50

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$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Which is not equal to slope?

© Mark E. Damon - All Rights Reserved

Congratulations!

You’ve ReachedYou’ve Reached

the $32,000the $32,000

Milestone!Milestone!

Congratulations!Congratulations!

© Mark E. Damon - All Rights Reserved

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: Positive

C: Zero

B: Negative

D: Undefined

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

How would you describe

the slope?

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© Mark E. Damon - All Rights Reserved

A: 1

C: Undefined

B: -1

D: 0

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

The slope of a vertical line is:

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: Undefined

C: Depends on points used to calculate it

B: 1

D: 0

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

The slope of a horizontal line is:

© Mark E. Damon - All Rights Reserved

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: Undefined

C: 2/3

B: -2/3

D: 0

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

Find the slope of the line passing through the points (-3,5) and

(-3,7)

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151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

© Mark E. Damon - All Rights Reserved

A: 3/2

C: 2

B: -1/4

D: 1/2

50:50

151413121110987654321

$1 Million$500,000$250,000$125,000$64,000$32,000$16,000$8,000$4,000$2,000$1,000$500$300$200$100

What is the slope of the equation

1/2x + 2y = 3?

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YOU WIN $1 MILLION DOLLARS!