I'm reading a Calculus book for my own edification and at the beginning the pre-calculus introduction has the problem,
They talk about solving the problem graphically, analytically, and numerically. The subject is the basic graph, Rene Descartes, etc.
They have numerical which is just a table of values. I understand that. Graph I understand.
But for the analytic approach, they have
"To systematically find other solutions, solve the original equation for $y$
I do not understand how they came up with that. Why not $x$? Why is this analytic? What makes this "analytic"? Why would it even occur to someone that solving for why is the way to go, the thought process.
I can solve the problem. That's not the issue. I want to understand why I'm doing it this way. Thanks.
"The Graph of an Equation
Consider the equation $3x+y=7$. The point $(2,1)$ is a solution point of the equation because the equation is satisfied (is true) when $2$ is substituted for $x$ and $1$ is substituted for $y$. This equation has many other solutions, such as $(1,4)$ and $(0,7)$. To systematically find other solutions solve the original equation for $y$.
$y = 7 - 3x$ Analytic approach"
I'm sure this is obvious and maybe I don't understand what the word analytic means in this context.
Calculus of a Single Variable, Sixth Edition, 1998, Larson, Hostetler, Edwards
(I got it a thrift store.)