integrated math 2 section 6-2
DESCRIPTION
Slope of a LineTRANSCRIPT
Section 6-2Slope of a Line
Thursday, November 12, 2009
Essential QuestionsHow do you find the slope of a line?
How do you identify horizontal and vertical lines?
Where you’ll see it:
Business, science, transportation
Thursday, November 12, 2009
Vocabulary1. Slope:
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Let’s try again.
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Let’s try again.
1. Slope:
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Let’s try again.
1. Slope: How steep a line is, measured in “rise over run”
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Let’s try again.
1. Slope: How steep a line is, measured in “rise over run”
Formula:
Thursday, November 12, 2009
Vocabulary1. Slope: The ratio of vertical distance change to
horizontal distance change
Let’s try again.
1. Slope: How steep a line is, measured in “rise over run”
Formula:
m =
y 2 −y1
x 2 − x1
, for points (x1 ,y1) and (x 2 ,y 2 )
Thursday, November 12, 2009
MATH CALISTHENICS!
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
m =
y 2 −y1
x 2 − x1
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
m =
y 2 −y1
x 2 − x1
=
4 − 04 − (−4)
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
m =
y 2 −y1
x 2 − x1
=
4 − 04 − (−4)
=
48
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
m =
y 2 −y1
x 2 − x1
=
4 − 04 − (−4)
=
48 =
12
Thursday, November 12, 2009
Example 1Graph the line the goes through the given points,
then find the slope of the line.
C = (−4,0)D = (4 ,4)
C
D
m =
y 2 −y1
x 2 − x1
=
4 − 04 − (−4)
=
48 =
12
Here, the slope tells us “Up 1, Right 2”Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
HorizontalThursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Horizontal
m =
y 2 −y1
x 2 − x1
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Horizontal
m =
y 2 −y1
x 2 − x1
=−4 −12
3 − 3
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Horizontal
m =
y 2 −y1
x 2 − x1
=−4 −12
3 − 3
=−16
0
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Horizontal
m =
y 2 −y1
x 2 − x1
=−4 −12
3 − 3
=−16
0Undefined
Thursday, November 12, 2009
Example 2Find the slope for the line containing the following:
a. (9, -2), (3, -2) b. (3, 12), (3, -4)
m =
y 2 −y1
x 2 − x1
=−2 − (−2)
3 − 9
=
0−6 = 0
Horizontal
m =
y 2 −y1
x 2 − x1
=−4 −12
3 − 3
=−16
0
Vertical
Undefined
Thursday, November 12, 2009
Horizontal vs. Vertical
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of zero
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of zero
(Think “horizon”)
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of zero
(Think “horizon”)
Vertical lines have a slope that is
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of zero
(Think “horizon”)
Vertical lines have a slope that is undefined
Thursday, November 12, 2009
Horizontal vs. VerticalHorizontal lines have slopes of zero
(Think “horizon”)
Vertical lines have a slope that is undefined(It’s neither uphill, downhill, or level)
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 3Graph the line that passes through P = (-1, 1) and
has a slope of -2.
−2 =
−21
Down 2, right 1P
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1 =
2 − (−1)2 − 0
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1 =
32
=2 − (−1)
2 − 0
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1 =
32
m(CD ) =
y 2 −y1
x 2 − x1
=
2 − (−1)2 − 0
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1 =
32
m(CD ) =
y 2 −y1
x 2 − x1
=
2 − (−1)2 − 0
=
4 −1−1− (−3)
Thursday, November 12, 2009
Example 4a. Find the slope of AB and CD for the given points.
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)
m(AB ) =
y 2 −y1
x 2 − x1 =
32
m(CD ) =
y 2 −y1
x 2 − x1 =
32
=
2 − (−1)2 − 0
=
4 −1−1− (−3)
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
B
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
D
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
D
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
D
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
D
The lines are parallel.
Thursday, November 12, 2009
Example 4
A = (0,−1), B = (2,2), C = (−3,1), D = (−1,4)b. Graph the two lines. What do you notice?
A
BC
D
The lines are parallel.
They have the same slope.
Thursday, November 12, 2009
Homework
Thursday, November 12, 2009
Homework
“The power of imagination makes us infinite.” - John Muir
p. 250 #1-35 odd
Thursday, November 12, 2009