By Lia Servidio and Kelly Lively Slope By Lia Servidio and Kelly Lively

What is Slope? Slope is a measure of how steep a line is The 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

How to Find Slope From Two Points Identify the two points: (x1,y1) and (x2,y2) 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) If (x1,y1)=(6,10) and (x2,y2)=(-2,5)

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? Since the equation is already set equal to y, look for the constant next to the x. y=4x+7, m=4 What is the slope of the line 6x+3y=12? Set the equation equal to y: 3y=-6x+12 y=-2x+4 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

Welcome to Who Wants to be a Millionaire 50:50 15 $1 Million 14 $500,000 Welcome to Who Wants to be a Millionaire 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Another Presentation © 2002 - All rights Reserved Mark E. Damon nygiantsbigblue@yahoo.com

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope of the line through the pair of points: 15 $1 Million 14 $500,000 13 $250,000 Find the slope of the line through the pair of points: (-4,7),(-6,-4) 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: -11/2 B: 11/2 C: -1 D: 2/11

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope: y=-5x-7 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 Find the slope: y=-5x-7 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 5/7 B: 5 C: -7 D: -5

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope of the line through the pair of points: 15 $1 Million 14 $500,000 Find the slope of the line through the pair of points: (19,3),(2,3) 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 0 B: 1 C: -1 D: Undefined

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope: 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 2/3 B: 3/2 C: - 1/2 D: 2

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope of the line through the pair of points: 15 $1 Million 14 $500,000 13 $250,000 Find the slope of the line through the pair of points: (17,-13),(17,8) 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 0 B: 1 C: Undefined D: -1

You’ve Reached the $1,000 Milestone! Congratulations! Congratulations!

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope: 8x+3y=-9 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 Find the slope: 8x+3y=-9 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 9/8 B: -8/3 C: 3/8 D: -1/3

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

What is the slope of this line? 15 $1 Million What is the slope of this line? 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 3/2 B: Undefined C: 1 D: 0

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Find the slope: x=-1 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: Undefined B: 0 C: 1 D: -1

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

What letter is commonly used to represent slope? 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 What letter is commonly used to represent slope? 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: k B: x C: m D: y

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

Which is not equal to slope? 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 Which is not equal to slope? 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: Rise/Run B: (y2-y1)/(x2-x1) C: ΔY/ ΔX D: Run/Rise

You’ve Reached the $32,000 Milestone! Congratulations!

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

How would you describe the slope? 15 $1 Million 14 $500,000 How would you describe the slope? 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: Positive B: Negative C: Zero D: Undefined

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

The slope of a vertical line is: 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 The slope of a vertical line is: 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 1 B: -1 C: Undefined D: 0

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

The slope of a horizontal line is: 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 The slope of a horizontal line is: 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: Undefined B: 1 C: Depends on points used to calculate it D: 0

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 Find the slope of the line passing through the points (-3,5) and (-3,7) 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: Undefined B: -2/3 C: 2/3 D: 0

15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 1 $100

What is the slope of the equation 1/2x + 2y = 3? 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 What is the slope of the equation 1/2x + 2y = 3? 11 $64,000 10 $32,000 9 $16,000 8 $8,000 7 $4,000 6 $2,000 5 $1,000 4 $500 3 $300 2 $200 50:50 1 $100 A: 3/2 B: -1/4 C: 2 D: 1/2

YOU WIN $1 MILLION DOLLARS!