simplify
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2 3. Exercise. Simplify. 4 − 2 5 − 2. 3 2. Exercise. Simplify. 5 − 2 4 − 2. Exercise. Simplify. 2 3. 2 − 4 5 − 2. –. 2 3. Exercise. Simplify. 2 − 4 2 − 5. Exercise. Simplify. 2 − 2 5 − 2. 0. Exercise. Simplify. 4 − 2 2 − 2. undefined. Rise. - PowerPoint PPT PresentationTRANSCRIPT
Simplify.Simplify.ExerciseExercise
4 − 25 − 24 − 25 − 2
2323
Simplify.Simplify.
5 − 24 − 25 − 24 − 2
3232
ExerciseExercise
Simplify.Simplify.
2 − 45 − 22 − 45 − 2
ExerciseExercise
2323
– –
Simplify.Simplify.
2 − 42 − 52 − 42 − 5
2323
ExerciseExercise
Simplify.Simplify.
2 − 25 − 22 − 25 − 2 00
ExerciseExercise
Simplify.Simplify.
4 − 22 − 24 − 22 − 2 undefinedundefined
ExerciseExercise
The rise is the vertical change from point P1 to point P2 on a line.
The rise is the vertical change from point P1 to point P2 on a line.
RiseRise
The run is the horizontal change from point P1 to point P2 on a line.
The run is the horizontal change from point P1 to point P2 on a line.
RunRun
The slope of a line is the ratio of the rise to the run. The variable m is often used for slope.
The slope of a line is the ratio of the rise to the run. The variable m is often used for slope.
SlopeSlope
yy
xx
yy
xx
up to right positive
down to right negative
horizontal zero
vertical undefined
SlopeSlope
Slope = m = Slope = m = riserunriserun
yy
xx−3−3
1 1
Find the slope of the given line.Find the slope of the given line.
m = = −3m = = −3−31
−31
Example 1Example 1
If a line contains the points P2 (x2, y2) and P1 (x1, y1),
then m = vertical change y2 − y1 horizontal change x2 − x1
vertical change y2 − y1 horizontal change x2 − x1
==
Slope FormulaSlope Formula
Find the slope of the line that contains the points (1, 2) and (7, 5).
Find the slope of the line that contains the points (1, 2) and (7, 5).
m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1
5 − 2
7 − 1
5 − 2
7 − 1== 3636
== 1212
Example 2Example 2
Find the slope of CD passing through (5, 3) and (2, 5).Find the slope of CD passing through (5, 3) and (2, 5).
m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1
5 − 3
2 − 5
5 − 3
2 − 5== 2−32
−3= −= − 2
323
Example 3Example 3
Find the slope of EF passing through (3, 2) and (−1, 2).Find the slope of EF passing through (3, 2) and (−1, 2).
m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1
2 − 2 −1 − 32 − 2
−1 − 3
== 0−40
−4= 0= 0
Example 4Example 4
yy
xx
(−1, 2)(−1, 2) (3, 2)(3, 2)
== 4040
Find the slope of the line passing through the points (2, 1) and (2, 5).
Find the slope of the line passing through the points (2, 1) and (2, 5).
m = =m = =y2 − y1 x2 − x1 y2 − y1 x2 − x1
5 − 1
2 − 2
5 − 1
2 − 2
Example 5Example 5
yy
xx
(2, 5)(2, 5)
(2, 1)(2, 1)
m = 3m = 3
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
y = 3x + 5y = 3x + 5
ExampleExample
1212
y = − x + 2y = − x + 2
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
m = −m = − 1212
ExampleExample
2323
y = x − 1y = x − 1
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
m = m = 2323
ExampleExample
m = 0m = 0
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
y = 4y = 4
ExampleExample
m = −3m = −3
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
y = −3x + 6y = −3x + 6
ExampleExample
undefinedundefined
Graph and determine the slope of the following lines.Graph and determine the slope of the following lines.
x = 4x = 4
ExampleExample
They are the same.They are the same.
Compare the slopes of the lines in the previous questions to the coefficients of x.
Compare the slopes of the lines in the previous questions to the coefficients of x.
ExampleExample
m =m = 5252
Find the slope of the line through (3, 7) and (5, 12).Find the slope of the line through (3, 7) and (5, 12).
ExampleExample
m = −6m = −6
Find the slope of the line through (2, 3) and (4, −9).Find the slope of the line through (2, 3) and (4, −9).
ExampleExample
m = 0m = 0
Find the slope of the line through (2, 5) and (3, 5).Find the slope of the line through (2, 5) and (3, 5).
ExampleExample
m = undefinedm = undefined
Find the slope of the line through (1, 1) and (1, 2).Find the slope of the line through (1, 1) and (1, 2).
ExampleExample
Their slopes are the same and the lines are parallel.Their slopes are the same and the lines are parallel.
Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2.
Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2.
ExampleExample