slope (algebra 2)
DESCRIPTION
Students learn the definition of slope and calculate the slope of lines. Students also learn to consider the slopes of parallel lines and perpendicular lines.TRANSCRIPT
![Page 1: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/1.jpg)
![Page 2: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/2.jpg)
Find and use the slope of a line.
Graph parallel and perpendicular lines.
1) slope2) rate of change
SlopeSlope
![Page 3: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/3.jpg)
If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree?
![Page 4: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/4.jpg)
Consider the options:
1) Keep the same slope of his / her path.
![Page 5: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/5.jpg)
Consider the options:
1) Keep the same slope of his / her path.
![Page 6: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/6.jpg)
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
![Page 7: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/7.jpg)
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.
![Page 8: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/8.jpg)
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.
![Page 9: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/9.jpg)
Consider the options:
1) Keep the same slope of his / her path.Not a good choice!
2) Go straight up.
Not possible! This is an airplane, not a helicopter.
![Page 10: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/10.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
![Page 11: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/11.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
![Page 12: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/12.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
![Page 13: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/13.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
vertical change
horizontal change
ySlope
x
![Page 14: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/14.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
vertical change
horizontal change
ySlope
x
![Page 15: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/15.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
vertical change
horizontal change
ySlope
x
![Page 16: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/16.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
vertical change
horizontal change
ySlope
x
![Page 17: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/17.jpg)
Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” requiredand divide that by the “horizontal change” required.
y
x
vertical change
horizontal change
ySlope
x
![Page 18: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/18.jpg)
vertical change 4,000 4 2
horizontal change 10,000 10 5
y ftSlope
x ft
y
x10000
10000
00
y
x
![Page 19: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/19.jpg)
x
y
FINDING THE SLOPE OF A LINE
SlopeSlope
![Page 20: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/20.jpg)
x
y
FINDING THE SLOPE OF A LINE
The slope m of the non-vertical linepassing through the pointsand is
1 1( , )x y
2 2( , )x y
1 1( , )x y
2 2( , )x y
SlopeSlope
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x
y
FINDING THE SLOPE OF A LINE
rise
runm
The slope m of the non-vertical linepassing through the pointsand is
1 1( , )x y
2 2( , )x y
1 1( , )x y
2 2( , )x y
SlopeSlope
![Page 22: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/22.jpg)
x
y
FINDING THE SLOPE OF A LINE
rise
runm
The slope m of the non-vertical linepassing through the pointsand is
1 1( , )x y
2 2( , )x y
1 1( , )x y
2 2( , )x y
ychange in
change x in
SlopeSlope
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x
y
2 1x x
FINDING THE SLOPE OF A LINE
rise
runm
The slope m of the non-vertical linepassing through the pointsand is
1 1( , )x y
2 2( , )x y
1 1( , )x y
2 2( , )x y
2 1y yychange in
change x in 2 1
2 1x x
y y
SlopeSlope
![Page 24: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/24.jpg)
x
y
2 1x x
FINDING THE SLOPE OF A LINE
rise
runm
The slope m of the non-vertical linepassing through the pointsand is
1 1( , )x y
2 2( , )x y
1 1( , )x y
2 2( , )x y
2 1y yychange in
change x in 2 1
2 1x x
y y
SlopeSlope
![Page 25: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/25.jpg)
y
x
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
(1, 1)
(3, 6)
SlopeSlope
![Page 26: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/26.jpg)
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
slope = =rise y
mrun x
SlopeSlope
![Page 27: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/27.jpg)
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
slope = =rise y
mrun x
SlopeSlope
![Page 28: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/28.jpg)
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
rise = 6 - 1 = 5 units
slope = =rise y
mrun x
SlopeSlope
![Page 29: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/29.jpg)
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
run = 3 - 1 = 2 units
rise = 6 - 1 = 5 units
slope = =rise y
mrun x
SlopeSlope
![Page 30: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/30.jpg)
The slope m of a non-vertical line is the number of units the line rises or fallsfor each unit of horizontal change from left to right.
y
x
(1, 1)
(3, 6)
run = 3 - 1 = 2 units
rise = 6 - 1 = 5 units
slope = =rise y
mrun x
5
=2
SlopeSlope
![Page 31: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/31.jpg)
y
x
SlopeSlope
Find the slope of the line.
(2, 3)
(8, 8)
![Page 32: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/32.jpg)
y
x
SlopeSlope
Find the slope of the line.
(2, 3)
(8, 8)
riseslope =
run
![Page 33: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/33.jpg)
y
x
SlopeSlope
Find the slope of the line.
(2, 3)
(8, 8)
run = 8 - 2 = 6 units
rise = 8 - 3 = 5 units
riseslope =
run
![Page 34: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/34.jpg)
y
x
SlopeSlope
Find the slope of the line.
(2, 3)
(8, 8)
run = 8 - 2 = 6 units
rise = 8 - 3 = 5 units
riseslope =
run
5=
6
![Page 35: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/35.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
SlopeSlope
![Page 36: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/36.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 37: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/37.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 38: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/38.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
2 1
2 1x
ym
y
x
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 39: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/39.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
2 1
2 1x
ym
y
x
4 (
1
)
7
4
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 40: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/40.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
-8
8
2 1
2 1x
ym
y
x
4 (
1
)
7
4
8
8
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 41: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/41.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
-8
8
2 1
2 1x
ym
y
x
4 (
1
)
7
4
8
8
1
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 42: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/42.jpg)
Plot the points (-4, 7) and (4, -1) and draw a line through them.Find the slope of the line passing through the points.
y
x
10
0
-5-5
5
-5
10
-5
0
5
1 1 1( , ) ( 4,7)P x y 2 2 2( , ) (4, 1)P x y
-8
8
2 1
2 1x
ym
y
x
4 (
1
)
7
4
8
8
1
Negative slope: Falls from left to right
1( 4,7)P
2 (4, 1)P
SlopeSlope
![Page 43: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/43.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
SlopeSlope
![Page 44: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/44.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
SlopeSlope
![Page 45: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/45.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
SlopeSlope
![Page 46: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/46.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
SlopeSlope
![Page 47: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/47.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
SlopeSlope
![Page 48: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/48.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
SlopeSlope
![Page 49: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/49.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
3) Draw the line, connecting the two points.
SlopeSlope
![Page 50: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/50.jpg)
y
x
Graph the line passing through point(1, 1) with a slope of 2.
1) Graph the point (1, 1).
2) Follow the slope of to locate another point on the line. 1
2
3) Draw the line, connecting the two points.
SlopeSlope
![Page 51: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/51.jpg)
y
x
If the line rises to the right,then the slope is positive.
SlopeSlope
![Page 52: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/52.jpg)
y
x
If the line rises to the right,then the slope is positive.
SlopeSlope
![Page 53: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/53.jpg)
y
x
If the line rises to the right,then the slope is positive.
y
x
If the line falls to the right,then the slope is negative.
SlopeSlope
![Page 54: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/54.jpg)
y
x
If the line rises to the right,then the slope is positive.
y
x
If the line falls to the right,then the slope is negative.
SlopeSlope
![Page 55: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/55.jpg)
y
x
If the line is horizontal,then the slope is zero.
SlopeSlope
![Page 56: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/56.jpg)
y
x
If the line is horizontal,then the slope is zero.
SlopeSlope
![Page 57: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/57.jpg)
y
x
If the line is horizontal,then the slope is zero.
y
x
If the line is vertical,then the slope is undefined.
SlopeSlope
![Page 58: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/58.jpg)
y
x
If the line is horizontal,then the slope is zero.
y
x
If the line is vertical,then the slope is undefined.
SlopeSlope
![Page 59: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/59.jpg)
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel.
![Page 60: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/60.jpg)
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel.with the same slope
![Page 61: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/61.jpg)
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel.with the same slope
![Page 62: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/62.jpg)
SlopeSlope
y
x
In a plane, nonvertical lines _________________ are parallel.with the same slope
![Page 63: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/63.jpg)
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.
SlopeSlope
![Page 64: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/64.jpg)
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
SlopeSlope
![Page 65: Slope (Algebra 2)](https://reader035.vdocument.in/reader035/viewer/2022062405/5559caeed8b42a98208b47c0/html5/thumbnails/65.jpg)
y
x
In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
SlopeSlope
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In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________.negative reciprocal
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Using Glencoe’s Algebra 2 text,© 2005
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