Linear Interpolation and Extrapolation

Key Questions

  • Why do you use linear extrapolation?

    Linear extrapolation is used to answer certain questions like:

    (insert name here) and (insert name here) start a (insert business thingy here) business and start with $2,000 per year. They get more customers each year. For each they they continue to work, they gain $2,000 more than the last year, and then they take away the cost of materials, $500.

    The equation is:

    #2,000X-500=Y#

    Pretend that there is a graph that lasts 20 years. Now, figure out how much money they will have after 30 years.

    By the way, that's:

    #2,000(30)-500=Y#

    #60,000-500=Y#

    #59,500=Y#

    Firelight · 1 · Nov 9 2014
  • How do you use the method of linear interpolation to approximate values and create an equation of a line?

    Let's say you have two points: #(x,y)# co-ordinates.

    An equation of the line will be of the form #y=m*x+b#
    where #m=# the slope and #b=# the so-called #y-#intercept.

    Example :
    Let's take #(-6,0)# and #(4,5)#
    graph{0.5x+3 [-9.61, 12.89, -2.795, 8.455]}
    Then first we determine the slope #m#
    Difference in #y=Deltay=5-0=5#
    Difference in #x=Deltax=4-(-6)=10#
    To find the slope we divide #(Deltay)/(Deltax)=5/10=1/2#

    We fill this in in one of the points to get #b#

    #y=mx+b->0=1/2*(-6)+b->b=+3#

    So the equation goes #y=1/2 *x+3#
    And you can fill in any #x# to get the #y#

    Check (allways check!) with the other point #(4,5)#:
    #1/2*4+3=5# is OK

    MeneerNask · 1 · Mar 22 2015

Questions

Forms of Linear Equations