Graphing linear equations
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Graphing linear equations

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Graphing linear equations Graphing linear equations Presentation Transcript

  • Graphing Linear Equations
  • Linear Equations are most often expressed in one of three forms:
    Slope-Intercept Form: 𝑦=π‘šπ‘₯+𝑏,
    Point-Slope Form: π‘¦βˆ’π‘¦1=π‘š(π‘₯βˆ’π‘₯1), and
    Standard Form: 𝐴π‘₯+𝐡𝑦=𝐢.
    Each form allows for quick and easy ways to graph the line they represent.
    Β 
    Forms of Linear Equations
  • One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=π‘šπ‘₯+𝑏).
    The steps are:
    Assign a value to the x-variable,
    Calculate the corresponding value for the y-coordinate, and
    Repeat.
    In this way, we can create a table of ordered pairs and plot them on the coordinate plane.
    Β 
    Make a Table
  • Consider the equation 𝑦=12π‘₯+2.
    Β 
    Make a Table
    𝑦=12(βˆ’πŸ)+2
    Β 
    (-2,1)
    =1
    𝑦=12(𝟎)+2
    Β 
    =2
    (0, 2)
    𝑦=12(𝟐)+2
    Β 
    (2, 3)
    =3
  • Another method for graphing lines when an equation is in slope-intercept form is as follows:
    Plot the y-intercept on the coordinate plane; that's the point (0, b).
    Use the slope to find another point (and repeat).
    Draw a line through the points.
    Use the slope and intercept
  • Consider the equation𝑦=βˆ’54π‘₯+7.
    Β 
    Plot the y-intercept
    Use the slope to find another point (and repeat).
    Draw a line through the points.
    Use the slope and intercept
    (0, b) = (0, 7)
    From the intercept, move down 5 and right 4 (or up 5 and left 4).
  • This method is very similar to the slope-intercept method. To graph a line using this method, do the following:
    Plot the point (π‘₯1, 𝑦1).
    Use the slope to find another point (and repeat).
    Draw a line through the points.
    Β 
    Use a point and the slope
  • Consider the equationπ‘¦βˆ’2=73(π‘₯+3).
    Β 
    Plot the point (π‘₯1, 𝑦1)
    Use the slope to find another point (and repeat).
    Draw a line through the points.
    Β 
    Use a point and the slope
    (π‘₯1, 𝑦1)= (-3, 2)
    Β 
    From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
  • This method is used when the line is in Standard Form (𝐴π‘₯+𝐡𝑦=𝐢).
    The x-intercept is easily calculated by setting y to 0 and solving for π‘₯.
    The y-intercept is calculated by setting π‘₯ to zero and solving for 𝑦.
    Plot the two intercepts and draw a line through them.
    Β 
    Use the Intercepts
  • Consider the equation3π‘₯βˆ’5𝑦=βˆ’15.
    Β 
    Set 𝑦=0 and solve for π‘₯.
    Set π‘₯=0 and solve for 𝑦.
    Draw a line through the points.
    Β 
    Use the Intercepts
    3π‘₯=βˆ’15; π‘₯=βˆ’5(βˆ’5,Β 0)
    Β 
    βˆ’5π‘₯=βˆ’15; 𝑦=3(0,Β Β 3)
    Β