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Slope By Lia Servidio and Kelly Lively

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What is Slope? Slope is a measure of how steep a line is The greater the slope value, the steeper the line

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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

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How to Find Slope From Two Points 1. Identify the two points: (x 1,y 1 ) and (x 2,y 2 ) 2. Use the formula m=(y 2 -y 1 )/(x 2 -x 1 ) *It does not matter which set of coordinates are considered to be (x 1,y 1 ) and which are considered to be (x 2,y 2 )

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Example What is the slope between the points (-2,5) and (6,10)? If (x 1,y 1 )=(-2,5) and (x 2,y 2 )=(6,10) If (x 1,y 1 )=(6,10) and (x 2,y 2 )=(-2,5)

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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

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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? 1. Set the equation equal to y: 3y=-6x+12 y=-2x+4 2. Look for the constant next to the x, m=-2

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How to Find Slope Using a Graph

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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

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15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved Another Presentation © 2002 - All rights Reserved nygiantsbigblue@yahoo.com

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© Mark E. Damon - All Rights Reserved

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15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: -11/2 C: -1 B: 11/2 D: 2/11 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 5/7 C: -7 B: 5 D: -5 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 0 C: -1 B: 1 D: Undefined 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 2/3 C: - 1/2 B: 3/2 D: 2 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 0 C: Undefined B: 1 D: -1 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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)

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© Mark E. Damon - All Rights Reserved Congratulations! You’ve Reached the $1,000 Milestone! Congratulations! C o n g r a t u l a t i o n s !

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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 9/8 C: 3/8 B: -8/3 D: -1/3 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 3/2 C: 1 B: Undefined D: 0 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: Undefined C: 1 B: 0 D: -1 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: k C: m B: x D: y 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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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 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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?

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© Mark E. Damon - All Rights Reserved Congratulations! You’ve Reached the $32,000 Milestone! Congratulations! C o n g r a t u l a t i o n s !

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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: Positive C: Zero B: Negative D: Undefined 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 1 C: Undefined B: -1 D: 0 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: Undefined C: Depends on points used to calculate it B: 1 D: 0 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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:

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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: Undefined C: 2/3 B: -2/3 D: 0 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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

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© Mark E. Damon - All Rights Reserved A: 3/2 C: 2 B: -1/4 D: 1/2 50:50 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 $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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© Mark E. Damon - All Rights Reserved YOU WIN $1 MILLION DOLLARS!

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