How do you use the method of linear interpolation to approximate values and create an equation of a line?

1 Answer
MeneerNask
Mar 22, 2015

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

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