SlideShare a Scribd company logo
1 of 16
Algebra II Chapter 2 Functions, Equations, and Graphs
©Tentinger
 Essential Understanding: If you move from any point
  on a nonvertical line in the coordinate plane to any
  other point on the line, the ratio of the vertical change
  to the horizontal change is constant. The constant
  ratio is the slope of the line.
 The slopes of two lines in the same plane indicate how
  the lines are related.
   Objectives
     Students will be able to graph linear equations
     Students will be able to write equations of lines
     Students will be able to write an equation of a line given its
      slope and a point on the line
   Algebra
   A-CED.2. Create equations in two or more variables to represent
    relationships between quantities; graph equations on coordinate axes
    with labels and scales.
   Functions
   F.IF.4. For a function that models a relationship between two quantities,
    interpret key features of graphs and tables in terms of the quantities, and
    sketch graphs showing key features given a verbal description of the
    relationship.★
   F-IF.7. Graph functions expressed symbolically and show key features of
    the graph, by hand in simple cases and using technology for more
    complicated cases.★
   F-IF.8. Write a function defined by an expression in different but
    equivalent forms to reveal and explain different properties of the
    function.
   F-IF.9. Compare properties of two functions each represented in a
    different way (algebraically, graphically, numerically in tables, or by
    verbal descriptions).
   What is slope?
   The ratio of vertical change to horizontal
    change between two lines.
   Find the slope of the line that passes through
    the given points.
   (5, 4) and ( 8, 1)
   (2, 2) and (-2, -2)
   (9, 3) and (9, -4)
   Does it matter what point you choose to be
    first when using the slope formula?
   How many different types of slopes are
    there?
   What is a linear function?
   What determines if a line is linear?
   What does a solution to a linear equation
    represent?
   What is a y-intercept?
   What is an x-intercept?
   There are two ways to represent a linear
    equation, what are they?
   y = mx + b


   What does each letter represent?
   What is the equation of the line with m = 6
    and y-intercept (0, 5)?
   Rewrite in slope-intercept form: 3x + 2y = 18
   What is the graph of 4x – 7y = 14?
   y – y1 = m(x – x1), where (x1, y1) is a point


   What is an equation of the line through (7, -1)
    with slope -3?
    A line passes through (-5, 0) and (0, 7). What
    is an equation of the line in point-slope form?
   Ax + By = C, where A and B are real numbers
    and are not both zero
   What is an equation of the line y = 9.1x +3.6 in
    standard form?


   What is the equation of the line y = (2/5)x – 3?
   Slope Intercept Form
     y = mx + b
     Use when you know the slope and the y – intercept
   Point Slope Form
     y – y1 = m(x – x1)
     Use when you know the slope and a point or if you
      know two points
   Standard Form
     Ax + By = C
   What are the intercepts of 2x – 4y = 8? Graph
    the equation.
   The office manager of a small office ordered
    140 packs of printer paper. Based on average
    daily use, she knows that the paper will last
    about 80 days.
     What graph represents this situation?
     What is the equation of the line in standard form?
     How many packs of a printer paper should the
     manager expect to have after 30 days?
   How do you know if two lines are parallel?
   Slopes are equal
   How do you know if two lines are
    perpendicular?
   Slopes are negative reciprocals
    (opposite re”flip”rocals)
   If you multiply the slopes
    together, it equals -1
   What is the equation of each line in slope-
    intercept form?
   The line parallel to 4x + 2y = 7 through (4, -2)


   The line perpendicular to y = (2/3)x – 1
    through (0, 6)
   Pg. 78
   # 9 – 39 (3’s), 47 - 49
   Pg. 86
   #3 – 42 (3’s)
   26 problems

More Related Content

What's hot

Parallel and Perpendicular lines
Parallel and Perpendicular linesParallel and Perpendicular lines
Parallel and Perpendicular lines
toni dimella
 
Parallel And Perpendicular Lines
Parallel And Perpendicular LinesParallel And Perpendicular Lines
Parallel And Perpendicular Lines
guestd1dc2e
 
6 4 Point Slope Form
6 4 Point Slope Form6 4 Point Slope Form
6 4 Point Slope Form
Kathy Favazza
 
Writing the equations of lines(point slope form)
Writing the equations of lines(point slope form)Writing the equations of lines(point slope form)
Writing the equations of lines(point slope form)
Apollo High School
 
Linear functions and modeling
Linear functions and modelingLinear functions and modeling
Linear functions and modeling
IVY SOLIS
 
Alg II 2-8 Inequalities
Alg II 2-8 InequalitiesAlg II 2-8 Inequalities
Alg II 2-8 Inequalities
jtentinger
 
matrices and function ( matrix)
matrices and function ( matrix)matrices and function ( matrix)
matrices and function ( matrix)
রেজা তানজিল
 
Review Of Slope And The Slope Intercept Formula
Review Of Slope And The Slope Intercept FormulaReview Of Slope And The Slope Intercept Formula
Review Of Slope And The Slope Intercept Formula
taco40
 
A2 1 linear fxns
A2 1 linear fxns A2 1 linear fxns
A2 1 linear fxns
vhiggins1
 
Algebra 1 Lesson Plan
Algebra 1 Lesson PlanAlgebra 1 Lesson Plan
Algebra 1 Lesson Plan
thoma3ca
 

What's hot (20)

Equations of a Line
Equations of a LineEquations of a Line
Equations of a Line
 
Parallel and Perpendicular lines
Parallel and Perpendicular linesParallel and Perpendicular lines
Parallel and Perpendicular lines
 
Parallel And Perpendicular Lines
Parallel And Perpendicular LinesParallel And Perpendicular Lines
Parallel And Perpendicular Lines
 
Matrix and Matrices
Matrix and MatricesMatrix and Matrices
Matrix and Matrices
 
6 4 Point Slope Form
6 4 Point Slope Form6 4 Point Slope Form
6 4 Point Slope Form
 
Writing the equations of lines(point slope form)
Writing the equations of lines(point slope form)Writing the equations of lines(point slope form)
Writing the equations of lines(point slope form)
 
Linear inequalities in two variables
Linear inequalities in two variablesLinear inequalities in two variables
Linear inequalities in two variables
 
Linear functions and modeling
Linear functions and modelingLinear functions and modeling
Linear functions and modeling
 
Alg II 2-8 Inequalities
Alg II 2-8 InequalitiesAlg II 2-8 Inequalities
Alg II 2-8 Inequalities
 
Topic 1
Topic 1Topic 1
Topic 1
 
matrices and function ( matrix)
matrices and function ( matrix)matrices and function ( matrix)
matrices and function ( matrix)
 
Review Of Slope And The Slope Intercept Formula
Review Of Slope And The Slope Intercept FormulaReview Of Slope And The Slope Intercept Formula
Review Of Slope And The Slope Intercept Formula
 
A2 1 linear fxns
A2 1 linear fxns A2 1 linear fxns
A2 1 linear fxns
 
2.3
2.32.3
2.3
 
Graphing lines
Graphing linesGraphing lines
Graphing lines
 
คาบ 2
คาบ 2คาบ 2
คาบ 2
 
Graph Period 2
Graph  Period 2Graph  Period 2
Graph Period 2
 
Lesson 1 - Introduction to Matrices
Lesson 1 - Introduction to MatricesLesson 1 - Introduction to Matrices
Lesson 1 - Introduction to Matrices
 
Calculus
CalculusCalculus
Calculus
 
Algebra 1 Lesson Plan
Algebra 1 Lesson PlanAlgebra 1 Lesson Plan
Algebra 1 Lesson Plan
 

Viewers also liked (6)

Final fiesta brodhead
Final fiesta   brodheadFinal fiesta   brodhead
Final fiesta brodhead
 
The truth about stress
The truth about stressThe truth about stress
The truth about stress
 
Final fiesta brodhead
Final fiesta   brodheadFinal fiesta   brodhead
Final fiesta brodhead
 
Eric Richard, the Birth of Tally
Eric Richard, the Birth of TallyEric Richard, the Birth of Tally
Eric Richard, the Birth of Tally
 
11.3 and11.5 Surface Area and Volume Pyramids
11.3 and11.5 Surface Area and Volume Pyramids11.3 and11.5 Surface Area and Volume Pyramids
11.3 and11.5 Surface Area and Volume Pyramids
 
Functional Prototype
Functional PrototypeFunctional Prototype
Functional Prototype
 

Similar to Alg II 2-3 and 2-4 Linear Functions

5.1 indentifying linear equations
5.1 indentifying linear equations5.1 indentifying linear equations
5.1 indentifying linear equations
coolhanddav
 
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docxLesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
SHIVA101531
 
5.1 Finding Slope
5.1 Finding Slope5.1 Finding Slope
5.1 Finding Slope
guest7985b1
 
Finding Slope 2009
Finding Slope 2009Finding Slope 2009
Finding Slope 2009
patrickhello
 
Alg II Unit 4-1 Quadratic Functions and Transformations
Alg II Unit 4-1 Quadratic Functions and TransformationsAlg II Unit 4-1 Quadratic Functions and Transformations
Alg II Unit 4-1 Quadratic Functions and Transformations
jtentinger
 
4 6 equations of lines
4 6 equations of lines4 6 equations of lines
4 6 equations of lines
gwilson8786
 
January 21, 2015
January 21, 2015January 21, 2015
January 21, 2015
khyps13
 
clmath8q2w4linearfunctions-211212103328.pdf
clmath8q2w4linearfunctions-211212103328.pdfclmath8q2w4linearfunctions-211212103328.pdf
clmath8q2w4linearfunctions-211212103328.pdf
mysthicrious
 
Linear_and_NonLinear_Functions_a (1).pptx
Linear_and_NonLinear_Functions_a (1).pptxLinear_and_NonLinear_Functions_a (1).pptx
Linear_and_NonLinear_Functions_a (1).pptx
AhmedMohamedMohamedE
 
vvvvvvvvvvvvvL2A_CurveRepresentations.pdf
vvvvvvvvvvvvvL2A_CurveRepresentations.pdfvvvvvvvvvvvvvL2A_CurveRepresentations.pdf
vvvvvvvvvvvvvL2A_CurveRepresentations.pdf
Khalil Alhatab
 

Similar to Alg II 2-3 and 2-4 Linear Functions (20)

5.1 indentifying linear equations
5.1 indentifying linear equations5.1 indentifying linear equations
5.1 indentifying linear equations
 
Chapter 5 Identifying Linear Functions
Chapter 5 Identifying Linear FunctionsChapter 5 Identifying Linear Functions
Chapter 5 Identifying Linear Functions
 
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptxWRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
 
Linear Equations in Two Variables.pptx
Linear Equations in Two Variables.pptxLinear Equations in Two Variables.pptx
Linear Equations in Two Variables.pptx
 
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docxLesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
Lesson 3-7 Equations of Lines in the Coordinate Plane 189.docx
 
5.1 Finding Slope
5.1 Finding Slope5.1 Finding Slope
5.1 Finding Slope
 
Finding slope
Finding slopeFinding slope
Finding slope
 
Finding Slope 2009
Finding Slope 2009Finding Slope 2009
Finding Slope 2009
 
Alg II Unit 4-1 Quadratic Functions and Transformations
Alg II Unit 4-1 Quadratic Functions and TransformationsAlg II Unit 4-1 Quadratic Functions and Transformations
Alg II Unit 4-1 Quadratic Functions and Transformations
 
4 6 equations of lines
4 6 equations of lines4 6 equations of lines
4 6 equations of lines
 
January 21, 2015
January 21, 2015January 21, 2015
January 21, 2015
 
8.3 Slope And Y Intercept
8.3 Slope And Y Intercept8.3 Slope And Y Intercept
8.3 Slope And Y Intercept
 
February 18 2016
February 18 2016February 18 2016
February 18 2016
 
Math 8 - Linear Functions
Math 8 - Linear FunctionsMath 8 - Linear Functions
Math 8 - Linear Functions
 
clmath8q2w4linearfunctions-211212103328.pdf
clmath8q2w4linearfunctions-211212103328.pdfclmath8q2w4linearfunctions-211212103328.pdf
clmath8q2w4linearfunctions-211212103328.pdf
 
7 1
7 17 1
7 1
 
American public university math 110 complete course
American public university math 110 complete courseAmerican public university math 110 complete course
American public university math 110 complete course
 
Linear_and_NonLinear_Functions_a (1).pptx
Linear_and_NonLinear_Functions_a (1).pptxLinear_and_NonLinear_Functions_a (1).pptx
Linear_and_NonLinear_Functions_a (1).pptx
 
vvvvvvvvvvvvvL2A_CurveRepresentations.pdf
vvvvvvvvvvvvvL2A_CurveRepresentations.pdfvvvvvvvvvvvvvL2A_CurveRepresentations.pdf
vvvvvvvvvvvvvL2A_CurveRepresentations.pdf
 
Fst ch2 notes
Fst ch2 notesFst ch2 notes
Fst ch2 notes
 

More from jtentinger

Geometry 1-7 Constructions
Geometry 1-7 ConstructionsGeometry 1-7 Constructions
Geometry 1-7 Constructions
jtentinger
 
Angle Sum Theorem
Angle Sum TheoremAngle Sum Theorem
Angle Sum Theorem
jtentinger
 
Bullying Prevention Certification
Bullying Prevention CertificationBullying Prevention Certification
Bullying Prevention Certification
jtentinger
 
Shipley - Algebra II Ch3 Proficiency Charts
Shipley - Algebra II Ch3 Proficiency ChartsShipley - Algebra II Ch3 Proficiency Charts
Shipley - Algebra II Ch3 Proficiency Charts
jtentinger
 
Shipley - Algebra II Ch2 Proficiency Charts
Shipley - Algebra II  Ch2 Proficiency ChartsShipley - Algebra II  Ch2 Proficiency Charts
Shipley - Algebra II Ch2 Proficiency Charts
jtentinger
 
Shipley - Semester 1 Summary Data
Shipley - Semester 1 Summary DataShipley - Semester 1 Summary Data
Shipley - Semester 1 Summary Data
jtentinger
 
Ch4 Matrices - How to use the Calculator
Ch4 Matrices - How to use the CalculatorCh4 Matrices - How to use the Calculator
Ch4 Matrices - How to use the Calculator
jtentinger
 
Pre-observation Form Oct 2013
Pre-observation Form Oct 2013Pre-observation Form Oct 2013
Pre-observation Form Oct 2013
jtentinger
 
Formal Observation/Notes October 2013
Formal Observation/Notes October 2013Formal Observation/Notes October 2013
Formal Observation/Notes October 2013
jtentinger
 
Algebra II Classroom and Homework Expectations
Algebra II Classroom and Homework ExpectationsAlgebra II Classroom and Homework Expectations
Algebra II Classroom and Homework Expectations
jtentinger
 
Sina workshop, day 1, january 25, 2013
Sina workshop, day 1, january 25, 2013Sina workshop, day 1, january 25, 2013
Sina workshop, day 1, january 25, 2013
jtentinger
 
Iowa Assessment Math Growth Rates Grades 7-11th
Iowa Assessment Math Growth Rates Grades 7-11thIowa Assessment Math Growth Rates Grades 7-11th
Iowa Assessment Math Growth Rates Grades 7-11th
jtentinger
 
Geometry Chapter 3 Test Scores and Retake Test
Geometry Chapter 3 Test Scores and Retake TestGeometry Chapter 3 Test Scores and Retake Test
Geometry Chapter 3 Test Scores and Retake Test
jtentinger
 
Alg II 3-6 Solving Systems - Matrices
Alg II 3-6 Solving Systems - MatricesAlg II 3-6 Solving Systems - Matrices
Alg II 3-6 Solving Systems - Matrices
jtentinger
 
Alg II 3-5 Sytems Three Variables
Alg II 3-5 Sytems Three VariablesAlg II 3-5 Sytems Three Variables
Alg II 3-5 Sytems Three Variables
jtentinger
 
Alg II 3-4 Linear Programming
Alg II 3-4 Linear ProgrammingAlg II 3-4 Linear Programming
Alg II 3-4 Linear Programming
jtentinger
 
Alg II 3-3 Systems of Inequalities
Alg II 3-3 Systems of InequalitiesAlg II 3-3 Systems of Inequalities
Alg II 3-3 Systems of Inequalities
jtentinger
 

More from jtentinger (20)

Geo 7-1 Ratios and Proportions
Geo 7-1 Ratios and ProportionsGeo 7-1 Ratios and Proportions
Geo 7-1 Ratios and Proportions
 
Geo 7-2 Similar Polygons
Geo 7-2 Similar PolygonsGeo 7-2 Similar Polygons
Geo 7-2 Similar Polygons
 
Geometry 1-7 Constructions
Geometry 1-7 ConstructionsGeometry 1-7 Constructions
Geometry 1-7 Constructions
 
Angle Sum Theorem
Angle Sum TheoremAngle Sum Theorem
Angle Sum Theorem
 
Bullying Prevention Certification
Bullying Prevention CertificationBullying Prevention Certification
Bullying Prevention Certification
 
Ethics
EthicsEthics
Ethics
 
Shipley - Algebra II Ch3 Proficiency Charts
Shipley - Algebra II Ch3 Proficiency ChartsShipley - Algebra II Ch3 Proficiency Charts
Shipley - Algebra II Ch3 Proficiency Charts
 
Shipley - Algebra II Ch2 Proficiency Charts
Shipley - Algebra II  Ch2 Proficiency ChartsShipley - Algebra II  Ch2 Proficiency Charts
Shipley - Algebra II Ch2 Proficiency Charts
 
Shipley - Semester 1 Summary Data
Shipley - Semester 1 Summary DataShipley - Semester 1 Summary Data
Shipley - Semester 1 Summary Data
 
Ch4 Matrices - How to use the Calculator
Ch4 Matrices - How to use the CalculatorCh4 Matrices - How to use the Calculator
Ch4 Matrices - How to use the Calculator
 
Pre-observation Form Oct 2013
Pre-observation Form Oct 2013Pre-observation Form Oct 2013
Pre-observation Form Oct 2013
 
Formal Observation/Notes October 2013
Formal Observation/Notes October 2013Formal Observation/Notes October 2013
Formal Observation/Notes October 2013
 
Algebra II Classroom and Homework Expectations
Algebra II Classroom and Homework ExpectationsAlgebra II Classroom and Homework Expectations
Algebra II Classroom and Homework Expectations
 
Sina workshop, day 1, january 25, 2013
Sina workshop, day 1, january 25, 2013Sina workshop, day 1, january 25, 2013
Sina workshop, day 1, january 25, 2013
 
Iowa Assessment Math Growth Rates Grades 7-11th
Iowa Assessment Math Growth Rates Grades 7-11thIowa Assessment Math Growth Rates Grades 7-11th
Iowa Assessment Math Growth Rates Grades 7-11th
 
Geometry Chapter 3 Test Scores and Retake Test
Geometry Chapter 3 Test Scores and Retake TestGeometry Chapter 3 Test Scores and Retake Test
Geometry Chapter 3 Test Scores and Retake Test
 
Alg II 3-6 Solving Systems - Matrices
Alg II 3-6 Solving Systems - MatricesAlg II 3-6 Solving Systems - Matrices
Alg II 3-6 Solving Systems - Matrices
 
Alg II 3-5 Sytems Three Variables
Alg II 3-5 Sytems Three VariablesAlg II 3-5 Sytems Three Variables
Alg II 3-5 Sytems Three Variables
 
Alg II 3-4 Linear Programming
Alg II 3-4 Linear ProgrammingAlg II 3-4 Linear Programming
Alg II 3-4 Linear Programming
 
Alg II 3-3 Systems of Inequalities
Alg II 3-3 Systems of InequalitiesAlg II 3-3 Systems of Inequalities
Alg II 3-3 Systems of Inequalities
 

Alg II 2-3 and 2-4 Linear Functions

  • 1. Algebra II Chapter 2 Functions, Equations, and Graphs ©Tentinger
  • 2.  Essential Understanding: If you move from any point on a nonvertical line in the coordinate plane to any other point on the line, the ratio of the vertical change to the horizontal change is constant. The constant ratio is the slope of the line.  The slopes of two lines in the same plane indicate how the lines are related.  Objectives  Students will be able to graph linear equations  Students will be able to write equations of lines  Students will be able to write an equation of a line given its slope and a point on the line
  • 3. Algebra  A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Functions  F.IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.★  F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★  F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.  F-IF.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • 4. What is slope?  The ratio of vertical change to horizontal change between two lines.
  • 5. Find the slope of the line that passes through the given points.  (5, 4) and ( 8, 1)  (2, 2) and (-2, -2)  (9, 3) and (9, -4)  Does it matter what point you choose to be first when using the slope formula?
  • 6. How many different types of slopes are there?
  • 7. What is a linear function?  What determines if a line is linear?  What does a solution to a linear equation represent?  What is a y-intercept?  What is an x-intercept?  There are two ways to represent a linear equation, what are they?
  • 8. y = mx + b  What does each letter represent?  What is the equation of the line with m = 6 and y-intercept (0, 5)?  Rewrite in slope-intercept form: 3x + 2y = 18  What is the graph of 4x – 7y = 14?
  • 9. y – y1 = m(x – x1), where (x1, y1) is a point  What is an equation of the line through (7, -1) with slope -3?  A line passes through (-5, 0) and (0, 7). What is an equation of the line in point-slope form?
  • 10. Ax + By = C, where A and B are real numbers and are not both zero  What is an equation of the line y = 9.1x +3.6 in standard form?  What is the equation of the line y = (2/5)x – 3?
  • 11. Slope Intercept Form  y = mx + b  Use when you know the slope and the y – intercept  Point Slope Form  y – y1 = m(x – x1)  Use when you know the slope and a point or if you know two points  Standard Form  Ax + By = C
  • 12. What are the intercepts of 2x – 4y = 8? Graph the equation.  The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days.  What graph represents this situation?  What is the equation of the line in standard form?  How many packs of a printer paper should the manager expect to have after 30 days?
  • 13. How do you know if two lines are parallel?  Slopes are equal
  • 14. How do you know if two lines are perpendicular?  Slopes are negative reciprocals (opposite re”flip”rocals)  If you multiply the slopes together, it equals -1
  • 15. What is the equation of each line in slope- intercept form?  The line parallel to 4x + 2y = 7 through (4, -2)  The line perpendicular to y = (2/3)x – 1 through (0, 6)
  • 16. Pg. 78  # 9 – 39 (3’s), 47 - 49  Pg. 86  #3 – 42 (3’s)  26 problems