Question

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

Answer 1

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