In article <fcednVlTC70BjyDanZ2dnUVZ_uGknZ2d@[EMAIL PROTECTED]
>,
OP <facetious_nickname@[EMAIL PROTECTED]
> wrote:
> On p. 58 & 59 of Spivak's Calculus, he says "Given two distinct
> points (a,b) and (c,d), find the linear function f whose graph goes
> through (a,b) and (c,d). This amounts to saying that f(a) = b and
> f(c) = d. If f is to be of the form f(x) = Aa + B, then we must have:
>
> Aa + B = b;
> Ac + B = d;
>
> therefore A = (d - b)/(c - a) and B = b - [(d - b)/(c - a)]a, so [etc.]"
>
> I substituted A for the alpha symbol and B for the beta symbol. My
> question is, why "therefore"? How does he pull the values of A and B
> out of those two equations? I understand where those two equations
> come from, but I don't get the derivation of A and B.
>
> This is not homework - which is a good thing, cause I'd flunking
> right about now.
>
> Thanks for any hints.
(Aa + B) - (Ac + B) = b - d
Aa - Ac = b - d
A = (b - d)/(a - c)
to start.
|
