How do you find the slope of a Quaderaterial Line?

[Q_Me]

How do you find "m" & "e" in the theory below?

y = m(x^e) + b

x1 = 1
y1 = 1

x2 = 2
y2 = 8

x3 = 3
x3 = 18

but what is the actual equation to find "m" and "e"?
eg.

mx^e = ?

how do you get "x" out of the first side?

m?^e = ?x?

[Q_Me]

If you know the Y1, X1, Y2, X2, Y3, X3, and B what is the rest of the problem?

[krtxmrtz]

If b is known, then the problem is not difficult.

Take, for example, the first 2 points,

y₁-b=mx₁^e
y₂-b=mx₂^e

Divide these two:

(y₁-b)/(y₂-b)=x₁^e/x₂^e=(x₁/x₂)^e

So now,

e log(x₁/x₂)=log((y₁-b)/(y₂-b))

e=log((y₁-b)/(y₂-b))/log(x₁/x₂)

and now m can be easily calculated.

If the (x,y) coordinates come from experimental measurements then probably not all 3 points will simultaneously comply with the equation so you'll have to try a fit by graphical or any other methods (least squares...?)

Originally posted by Q_Me
If you know the Y1, X1, Y2, X2, Y3, X3, and B what is the rest of the problem?