slope by lia servidio and kelly lively. what is slope? slope is a measure of how steep a line is the...
TRANSCRIPT
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
© 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)
© 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: 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
© 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: 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)
© 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: 2/3
C: - 1/2
B: 3/2
D: 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
Find the slope:
© 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: 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
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:
8x+3y=-9
© 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: 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?
© 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: 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
© 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: k
C: m
B: x
D: y
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 letter is commonly used to represent slope?
© 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: Rise/Run
C: ΔY/ ΔX
B: (y2-y1)/(x2-x1)
D: Run/Rise
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
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?
© 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: 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:
© 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: 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)
© 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: 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!