algebra ppt
DESCRIPTION
EDU 290 projectTRANSCRIPT
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Algebra 1- Slope
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Things that involve slope!
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Slope is the ratio between vertical rise and horizontal run between any 2 points on the same line.
Slope= vertical rise ÷ horizontal run
The Slope Ratio
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Find the slope of a hill that has a vertical rise of 40ft and a horizontal run of 200 ft.
(Let m represent slope)
Real Life Examples
Vertical Rise= 40 ft
Horizontal Run= 200 ft
m= vertical/horizontal
m= 40/200 = 1/5
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The slope m of a line that passes through points (x₁, y₁) and (x₂, y₂) is
The Slope of a Line
m=riserun=
change in ychange in x
y₂-y₁=x₂-x₁
Where (x₁, y₁) and (x₂, y₂) are any 2 points on the same line and x₁≠x₂.
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Let (x₁, y₁)= (1,0) and (x₂,y₂)=(3,4)Find m.
Positive Slope
y₂-y₁x₂-x₁
m= = 4-03-1
=24 =2
There is a positive slope of 2 therefore the line rises from left to right.
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Negative Slope
Let (x₁, y₁)= (0,3) and (x₂,y₂)=(4,1)
Find m.y₂-y₁x₂-x₁
m= = 1-34-0
=4-2
= -1
There is a negative slope of -1/2 therefore the line falls from left to right.
2
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Zero Slope
Let (x₁, y₁)= (1,2) and (x₂,y₂)=(4,2)Find m.
y₂-y₁x₂-x₁
m= = 2-24-1
=30 =0
There is a zero slope therefore the line is horizontal. We can compare this to walking across the floor.
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Undefined Slope
Let (x₁, y₁)= (3,-1) and (x₂,y₂)=(3,3)Find m.
y₂-y₁x₂-x₁
m= = 3-⁻15-5
=04 =Undefin
ed!The slope is undefined because division by 0 is undefined and the expression 4/0 has no meaning. This line is vertical and we can compare it to walking up a wall, impossible.
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Summary: Slope of Lines
Positive- rises left to right
Negative- falls left to right
Zero- horizontal
Undefined- vertical
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y=mx+b where m and b are constants, then the graph of that equation is a line with slope m and y-intercept b.
The bigger the slope, the steeper the line.
Even of you choose completely different points on the same line, the slope will remain constant.
Slope Intercept Form of a Line
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Example
Find the slope and y-intercept of the line and then graph the line.
3x + 5y −15 = 0
y= x+3
-35
Solve for y by subtracting 5y from both side and then divinding both sides by -5.
slope
y-intercept
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The top of the ladder is 12ft from the ground. The base of the ladder is 5ft from the wall. What is the slope of the ladder?
Ladder
rise 12run5
=12ft
5ft
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Making Sense of Slope!
A
D
CBE
Choose different pairs of points on the line and find their slope.What do you notice? What conclusion can you draw?
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Making Sense of Slope! Anwsers
mAB=
mBC=
mCD=
mDE=
12 12 12 12
Now, based on the conclusion that the slope is ½ between each set of points, complete the sentence:No matter what pair of points you choose on a line, the ______ remains constant.
*slope
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The Slope of the Road
The slope of the road is the vertical rise divided by the horizontal run. If the vertical rise is 24 feet for a horizontal run of 1 mile, determine the slope of the road. *Hint- 1 mile=5280 feet 24ft 24ft
1 1mi 5280ft 220
==
*This means that for every 1ft that you move up, you also move 220ft forward.
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CREDITS
Larson, Ron, Laurie Boswell, Timothy D. Kanold, and Lee Stiff. Algebra 1: Concepts and Skills. Teacher's ed. Evanston, IL: McDougal Littell, 2001. 229-233. Print.
Gustafson, R. David, and Peter D. Frisk. Beginning Algebra. Instructor's 3rd ed. Pacific Grove, CA: Brooks/Cole, 1992. 285-289. Print.
Håkan Dahlström, Six Flags Holland, 2/28/11 via Flickr, Creative Commons Attribution
Chad K., Hills Outside Silgo, 2/28/11 via Flickr, Creative Commons Attribution
Tony the Misfit, Snowboarding Along the East River, 2/28/11 via Flickr, Creative Commons Attribution
Pocius, Rooftops in Reykjavik, Iceland, 2/28/11 via Flickr, Creative Commons Attribution
Robert Couse-Baker, Up and Down the Ladder, 2/28/11 via Flickr, Creative Commons Attribution
Melissa, The Road Home, 2/28/11 via Flickr, Creative Commons Attribution