Linear Interpolation and Extrapolation
Key Questions

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:
#2,000X500=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# #60,000500=Y# #59,500=Y# 
Let's say you have two points:
#(x,y)# coordinates.An equation of the line will be of the form
#y=m*x+b#
where#m=# the slope and#b=# the socalled#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=50=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
Questions
Forms of Linear Equations

Write an Equation Given the Slope and a Point

Write an Equation Given Two Points

Write a Function in SlopeIntercept Form

Linear Equations in PointSlope Form

Forms of Linear Equations

Applications Using Linear Models

Equations of Parallel Lines

Equations of Perpendicular Lines

Families of Lines

Fitting Lines to Data

Linear Interpolation and Extrapolation

Problem Solving with Linear Models

Dimensional Analysis