lecture 161 unit 2 lecture 16 slope slope. lecture 162 objectives given two points, calculate the...
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Lecture 16Lecture 16 11
Unit 2 Lecture 16Unit 2 Lecture 16SlopeSlope
Slope
Lecture 16Lecture 16 22
ObjectivesObjectives
• Given two points, calculate the slope of the Given two points, calculate the slope of the line through those two pointsline through those two points
• Given the equation of a line, identify the Given the equation of a line, identify the slope and y intercept.slope and y intercept.
Lecture 16Lecture 16 33
Slope is rise over run.
Slope
Change in Ym
Change in X
1 0
1 0
Y -YChange in Ym
Change in X X -X
Lecture 16Lecture 16 44
Find the Slope of the line that passes through (6, -2) and (5, 7).
Slope
1 0
1 0
Y -YChange in Ym
Change in X X -X
1 0
1 0
Y -Y 9m 9
X -X 1
1 0
1 0
7Y -Y ( 2) 9m
X -X 65 1
Lecture 16Lecture 16 55
Plot the points and verify the slope of -9
2 4
4
2
-2
(6, -2)
(5, 7)
Lecture 16Lecture 16 66
Plot the points and verify the slope of -9
2 4
4
2
-2
(5, 7)
(6, -2)
Lecture 16Lecture 16 77
Find the Slope of the line that passes through (8, 2) and (4, -12).
Slope
1 0
1 0
Y -YChange in Ym
Change in X X -X
1 0
1 0
Y -Y ( ) 14 7m
X -X 4
2 21
4 28
1 0
1 0
Y -Y 7m 3.5
X -X 2
Lecture 16Lecture 16 88
Plot the points and verify the slope of 3.5
2 4
6
3
-3
-6
-9
-12
(8, 2)(4, -12)
Lecture 16Lecture 16 99
Plot the points and verify the slope of 3.5
2 4
6
3
-3
-6
-9
-12
(8, 2)(4, -12)
Lecture 16Lecture 16 1010
Find the Slope of the line that passes through (2, 4) and (2, -5).
Slope
1 0
1 0
Y -YChange in Ym
Change in X X -X
1 0
1 0
Y -Ym undefined
X -X
1 0
1 0
Y -Y ( ) 9m undefined
X -X 022
45
Lecture 16Lecture 16 1111
Plot the points and verify the slope.
1 2
2
1
-1
(2, 4)
(2, -5)
Lecture 16Lecture 16 1212
Plot the points and verify the slope.
1 2
2
1
-1
(2, -5)
(2, 4)
Lecture 16Lecture 16 1313
Find the Slope of the line that passes through (4, -3) and (-2, -3).
Slope
1 0
1 0
Y -YChange in Ym
Change in X X -X
1 0
1 0
Y -Ym 0
X -X
1 0
1 0
Y -Y ( ) 0m 0
X -X
3
6
3
42
Lecture 16Lecture 16 1414
Plot the points and verify the slope is 0.
1 2
2
1
-1
(4, -3)(-2, -3)
-2
Lecture 16Lecture 16 1515
Plot the points and verify the slope is 0.
1 2
2
1
-1
-2
(-2, -3)(4, -3)
Lecture 16Lecture 16 1616
Y=mx+bY=mx+b
mm
bb
Y= m x + bm = slope; b = y-intercept
35
4y x
Lecture 16Lecture 16 1717
Y=mx+bY=mx+b
mm -3/4-3/4
bb -5-5
Y= m x + bm = slope; b = y-intercept
35
4y x
Lecture 16Lecture 16 1818
35
4y x
Lecture 16Lecture 16 1919
2 4
4
2
-2
(0, -5)
(4, -8)
35
4y x
Lecture 16Lecture 16 2020
Y=mx+bY=mx+b
mm
bb
Y= m x + bm = slope; b = y-intercept
4 5y x
Lecture 16Lecture 16 2121
Y=mx+bY=mx+b
mm 44
bb 55
Y= m x + bm = slope; b = y-intercept
4 5y x
Lecture 16Lecture 16 2222
y = 4x + 5
Lecture 16Lecture 16 2323
1 2
4
2
-2
-4
6
8 (1, 9)(0, 5)
y = 4x + 5
Lecture 16Lecture 16 2424
y = 4x + 5
Lecture 16Lecture 16 2525
Solve for y in terms of x3x + 2y = 6
3x + 2y = 6
2y = 6-3x Subtract 3x from both sides
y = (6-3x)/2 Divide both sides by 2
Write in y = mx + b form3
32
y x
Lecture 16Lecture 16 2626
Y=mx+bY=mx+b
mm -3/2-3/2
bb +3+3
Y= m x + bm = slope; b = y-intercept
33
2y x
Lecture 16Lecture 16 2727
3x + 2y = 63
32
y x
Lecture 16Lecture 16 2828
1 2
2
1
-1
(0, 3)
(2, 0)
33
2y x