The Manga Guide to Calculus

The Basics of Variable Linear Functions 187

Since the sticks

become higher by

2 the further away

from us they are,

we find that the

tops of the sticks

as a whole form a

plane. We can now

generalize this.

First, let’s draw

the graph of

z = f(x, y) = ax + by

(letconstant c = 0 ).

Let’s consider a plane that

represents the function

f(x, y). We can start at

point O, which we know is

(0, 0, 0), or the origin. Now

consider line segment

OA—a function to describe

this line can be found if we

set y = 0. This means that

line is represented by the

functionz = ax, and has

slopea. Similarly, we find

that line segment OB of

this plane is represented

by t ...