Linear functions
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Linear functions

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Linear functions Linear functions Presentation Transcript

  • Linear Functions
  • Standard: Ax + By = C
    Point Slope: y - y₁ = m(x-x₁)
    Slope-Intercept: y = mx + b
    Slope: m = π‘¦Β βˆ’π‘¦β‚π‘₯Β βˆ’π‘₯₁
    Β 
    Linear Function Expressions and Forms
  • Converting between Forms
    Standard to Slope-Intercept
    Ax + By = C
    By = -Ax + C
    y = βˆ’π΄π‘₯+𝐢𝐡
    y = βˆ’π΄π‘₯𝐡 + C
    Let βˆ’π΄π΅ = m
    Let C = b
    y = mx + b
    Β 
    Point-Slope to Slope
    y - y₁ = m( x - x₁)
    π‘¦Β βˆ’π‘¦β‚π‘₯Β βˆ’π‘₯₁ = m
    m = π‘¦βˆ’π‘¦β‚π‘₯βˆ’π‘₯₁
    Β 
    View slide
  • Graphing Linear FunctionsUsing Points
    Use two points ( x, y) and ( x₁, y₁)
    Find these points on the graph
    For example:
    Let ( x, y) = ( 1, 2)
    and ( x₁, y₁) = ( 3, 4)
    View slide
  • Graphing Linear FunctionsUsing points
    To find Slope
    Count π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’ on graph
    Β 
    Or
    Use point-slope form
    Y - y₁ = m( x - x₁)
    2 - 4 = m( 1 - 3)
    πŸΒ βˆ’πŸ’πŸΒ βˆ’πŸ‘ = m
    m = βˆ’πŸβˆ’πŸ
    m = 1
    Slope is 1
    Β 
  • Graph 3y – 9x = 3
    First solve equation for y
    3y – 9x = 3
    3y + 9x – 9x = 3 + 9x
    πŸπŸ‘ βˆ™ 3y = 3 + 9x βˆ™ πŸπŸ‘
    y = 1 + 3x
    y = 3x + 1
    Equation is now in slope-intercept form
    Β 
    Graphing Linear FunctionsMaking a Table
  • Graphing Linear FunctionsMaking a Table
    Now select some values for domain
    Plug values into y = 3x + 1
  • Graphing Linear FunctionsMaking a Table
    Graph ordered pairs
    Draw line through points
  • Graphing Linear FunctionsUsing intercepts
    Find x-intercept of 7x + y = -4
    Replace y with zero
    7x + 0 = -4
    πŸπŸ• βˆ™ 7x + 0 = -4 βˆ™ πŸπŸ•
    x = βˆ’πŸ’πŸ•
    Β 
    Find y-intercept of 7x + y = -4
    Replace x with zero
    7(0) + y = -4
    y = -4
  • Graphing Linear FunctionsUsing intercepts
    X-intercept is βˆ’πŸ’πŸ•
    Line intersects x-axis at ( βˆ’πŸ’πŸ•, 0)
    Y-intercept is -4
    Line intersects y-axis at ( 0, -4)
    Β 
  • Find Equation of Function Using GraphsSlope-Intercept
    Find where line intersects y-axis
    This value is b
    Find slope of line by π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’
    This value is m
    y = mx + b
    Β 
  • Find Equation of Function Using GraphsPoint-Slope
    Plug given point into ( x₁, y₁ )
    y – 2 = m( x – 3)
    Find slope by π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’ in graph
    Plug slope into m
    y – 2 = 𝟏𝟐( x – 3)
    Β 
  • Parallel Linear Functions
    y = πŸ‘πŸ x + 1
    y = πŸ‘πŸ x + 4
    Are these functions parallel?
    Graph them
    They are parallel
    Β 
  • Perpendicular Linear Functions
    y = βˆ’πŸ‘πŸ’x + 2
    y = πŸ’πŸ‘ x + 3
    Are these functions perpendicular?
    Graph them
    They are Perpendicular
    Β 
  • Parallel and Perpendicular Linear Functions
    Parallel
    Functions with equal slopes are parallel
    y = mx + b
    y = πŸ‘πŸ x + 1
    y = πŸ‘πŸ x + 4
    m = πŸ‘πŸ
    Β 
    Perpendicular
    Functions with reciprocal slopes are perpendicular
    Y = mx + b
    Y = βˆ’πŸ‘πŸ’ x + 2
    Y = πŸ’πŸ‘ x + 3
    M = βˆ’πŸ‘πŸ’ and m = πŸ’πŸ‘
    Β 
  • TI-Nspire CAS Student Software, All TI-Nspire CAS Calculator images, September 22, 2010, Copy Righted Texas Instruments.
    Citations