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.
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