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Slope of a Line
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Slope of a Line
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Slope of a Line
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Slope of a Line
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Slope of a Line
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Slope of a Line
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Slope of a Line
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Slope of a Line
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+ Slope + slope
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+ Slope
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+ Slope
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+ Slope
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Slope = 0 + Slope Horizontal Slope = 0
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Slope = 0 + Slope Horizontal Slope = 0
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Slope = 0 + Slope Slope = Undefined Vertical Slope = Undefined
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Slope = 0 + Slope Slope = Undefined Vertical Slope = Undefined
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Slope = 0 + Slope - Slope = Undefined Slope - slope
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Slope = 0 + Slope - Slope = Undefined Slope - slope
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Slope = 0 + Slope - Slope = Undefined Slope
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+ Slope
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+ Slope
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_ Slope
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_ Slope
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Slope = 0
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Slope = 0
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Slope = undefined
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Slope = undefined
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_ Slope
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_ Slope
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+ Slope
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+ Slope
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Slope = undefined
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Slope = undefined
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Slope = 0
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Slope = 0
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
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Using a Table of Values to Graph Linear Equations
+ Slope
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How do engineers build bridges?
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Grade of a Road is the Same the Slope
7 feet Slope 100 feet
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Grade of a Road is the Same the Slope
7 feet Slope 100 feet
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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So How Can We Calculate the Slope of A line
Rise Rise = + 2 ___ Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
Rise Rise = + 2 ___ Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
2 Rise = + 2 ___ Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
2 Rise = + 2 ___ Slope = 1 Run = + 1
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So How Can We Calculate the Slope of A line
2 Rise = + 2 ___ Slope = 1 Run = + 1
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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So How Can We Calculate the Slope of A line
Fall ___ Slope = Run
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So How Can We Calculate the Slope of A line
Fall ___ Fall = - 2 Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
Fall ___ Fall = - 2 Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
-2 ___ Fall = - 2 Slope = Run Run = + 1
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So How Can We Calculate the Slope of A line
-2 ___ Fall = - 2 Slope = 1 Run = + 1
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So How Can We Calculate the Slope of A line
-2 ___ Fall = - 2 Slope = 1 Run = + 1
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ m = Run Run
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ m = Run Run
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So How Can We Calculate the Slope of A line
Rise Fall ___ or ___ Slope = Run Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Slope Y-intercept
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Graphing a Linear Equation
Slope Intercept Form y = m x + b b Slope Y-intercept m y = x + b
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Graphing a Linear Equation
Slope Intercept Form y = m x + b b Slope Y-intercept m y = x + b
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Graphing a Linear Equation
Slope Intercept Form y = m x + b b Slope Y-intercept m y = x + 4
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Graphing a Linear Equation
Slope Intercept Form y = m x + b b Slope Y-intercept Fall m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b b Slope Y-intercept Fall m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 Fall m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ Run
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ 2
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 - 4 m y = x + 4 m = ___ 2
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Graphing a Linear Equation
Slope Intercept Form y = m x + b Fall =-4 Slope Y-intercept Run = 2 m -2 y = x + 4 m =
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Graphing a Linear Equation
Slope Intercept Form y = -2 x + 4 y = m x + b Fall =-4 Slope Y-intercept Run = 2 -2 y = x + 4 m = -2
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Example 1 : Graph The Equation
y = 3/2 x + 6 y = m x + b b= 6 Rise 3 ____ m = = ____ Run 2
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Example 1 : Graph The Equation
y = 3/2 x + 6 Run = 2 Graph The Equation : Rise = 3 y = 3/2 x + 6 y = m x + b b= 6 Rise 3 ____ m = = ____ Run 2
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What is Standard Form? Standard Form Where A , B , C are numbers
A x + B y = C Standard Form Where A , B , C are numbers 2 x + 4 y = 6 5 x - 7 y = 12 3 x + 4 y = - 2
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What is Standard Form? Standard Form Where A , B , C are numbers
A x + B y = C Standard Form Where A , B , C are numbers 2 x + 4 y = 6 5 x - 7 y = 12 3 x + 4 y = - 2
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y = m x + b What is Standard Form? Standard Form Slope Intercept Form
A x + B y = C Standard Form Change to y = m x + b Slope Intercept Form 4 x + 2 y = 4 Standard Form
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What is Standard Form? A x + y = B C Standard Form
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What is Standard Form? 4 x + y = B C Standard Form
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What is Standard Form? 4 x + y = B C Standard Form
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What is Standard Form? 4 x + y = 2 C Standard Form
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What is Standard Form? 4 x + y = 2 C Standard Form
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What is Standard Form? 4 x + y = 2 4 Standard Form
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4 x + y = 2 4 -4x -4x 2 y = -4x +4 __ __ __ 2 2 2 -2 x + 2 y =
What is Standard Form? 4 x + y = 2 4 Standard Form -4x -4x _______________________ 2 y = -4x +4 __ __ __ 2 2 2 _______________________ -2 x + 2 y = y = m x + b Slope Intercept Form
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4 x + y = 2 4 -4x -4x 2 y = -4x +4 __ __ __ 2 2 2 -2 x + 2 y =
What is Standard Form? 4 x + y = 2 4 Standard Form -4x -4x _______________________ 2 y = -4x +4 __ __ __ 2 2 2 _______________________ -2 x + 2 y = y = m x + b Slope Intercept Form
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4 2 4 x + y = y = m x + b What is Standard Form? Standard Form
Slope Intercept Form
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What is Standard Form? 4 x + y = 2 2 Standard Form y = m x + b Slope Intercept Form b = 2 m = -2 = -2 __ 1
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Using the X and Y Intercept to Graph
X- Intercept : Any Point in X-Axis is going to have an Y= 0 Y- Intercept : Any Point in Y-Axis is going to have an X= 0
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= 8 2(0) + 4 y 2x + 4 = 8 4 y = 8 2x __ __ __ = 8 __ 4 4 2 2 = 2 4 y =
Using the X and Y Intercept to Graph = 8 2(0) + 4 y 2x + 4 = 8 (0) 4 y = 8 2x __ __ __ = 8 __ 4 4 2 2 = 2 4 y = x (4,0) (0,2) The X - Intercept is: The Y - Intercept is:
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= 8 2(0) + 4 y 2x + 4 = 8 4 y = 8 2x __ __ __ = 8 __ 4 4 2 2 = 2 4 y =
Using the X and Y Intercept to Graph = 8 2(0) + 4 y 2x + 4 = 8 (0) 4 y = 8 2x __ __ __ = 8 __ 4 4 2 2 = 2 4 y = x (4,0) (0,2) The X - Intercept is: The Y - Intercept is:
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Using the X and Y Intercept to Graph
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Using the X and Y Intercept to Graph
y = m x + b
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Using the X and Y Intercept to Graph
y = x + m b
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Using the X and Y Intercept to Graph
y = x + m 2
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y = x + m 2 m = = = Using the X and Y Intercept to Graph Fall -2 -1
___ ___ = ___ Run 4 2
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y = x + m 2 m = = = Using the X and Y Intercept to Graph Fall -2 -1
___ ___ = ___ Run 4 2
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y = x + 2 m = = = Using the X and Y Intercept to Graph -1 ___ 2 Fall
-2 -1 ___ ___ = ___ Run 4 2
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_ y2 – y1 7 2 _______ 5 _______ Slope = = = _ x2 – x1 3 5 2
Slope Formula If you are ask to find the slope given two points use The slope formula _ y2 – y1 7 2 _______ 5 _______ Slope = = = ___ _ x2 – x1 3 5 2 Find the slope between the points (3,2) and (5,7) x1 y1 x2 y2
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Exercises
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Exercises
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Exercises
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Exercises
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Exercises
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