slope by lia servidio and kelly lively. what is slope? slope is a measure of how steep a line is the...
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![Page 1: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/1.jpg)
Slope
By Lia Servidio and Kelly Lively
![Page 2: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/2.jpg)
What is Slope?
Slope is a measure of how steep a line isThe greater the slope value, the steeper
the line
![Page 3: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/3.jpg)
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
![Page 4: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/4.jpg)
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)
![Page 5: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/7.jpg)
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
![Page 8: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/8.jpg)
How to Find Slope Using a Graph
![Page 9: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/9.jpg)
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
![Page 10: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/10.jpg)
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
![Page 12: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/12.jpg)
© Mark E. Damon - All Rights Reserved
![Page 13: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/13.jpg)
© 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
![Page 14: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/14.jpg)
© 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)
![Page 15: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/15.jpg)
© 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
![Page 16: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/16.jpg)
© 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
![Page 17: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/17.jpg)
© 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
![Page 18: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/18.jpg)
© 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)
![Page 19: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/19.jpg)
© 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
![Page 20: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/20.jpg)
© 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:
![Page 21: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/21.jpg)
© 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
![Page 22: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/22.jpg)
© 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)
![Page 23: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/23.jpg)
© Mark E. Damon - All Rights Reserved
Congratulations!
You’ve ReachedYou’ve Reached
the $1,000the $1,000
Milestone!Milestone!
Congratulations!Congratulations!
![Page 24: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/24.jpg)
© 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
![Page 25: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/25.jpg)
© 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
![Page 26: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/26.jpg)
© 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
![Page 27: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/27.jpg)
© 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?
![Page 28: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/28.jpg)
© 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
![Page 29: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/29.jpg)
© 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
![Page 30: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/30.jpg)
© 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
![Page 31: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/31.jpg)
© 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?
![Page 32: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/32.jpg)
© 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
![Page 33: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/33.jpg)
© 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?
![Page 34: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/34.jpg)
© Mark E. Damon - All Rights Reserved
Congratulations!
You’ve ReachedYou’ve Reached
the $32,000the $32,000
Milestone!Milestone!
Congratulations!Congratulations!
![Page 35: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/35.jpg)
© 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
![Page 36: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/36.jpg)
© 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?
![Page 37: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/37.jpg)
© 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
![Page 38: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/38.jpg)
© 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:
![Page 39: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/39.jpg)
© 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
![Page 40: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/40.jpg)
© 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:
![Page 41: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/41.jpg)
© 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
![Page 42: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/42.jpg)
© 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)
![Page 43: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/43.jpg)
© 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
![Page 44: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/44.jpg)
© 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?
![Page 45: 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](https://reader036.vdocuments.site/reader036/viewer/2022062511/551bda8d550346be588b5a31/html5/thumbnails/45.jpg)
© Mark E. Damon - All Rights Reserved
YOU WIN $1 MILLION DOLLARS!