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