Question

How can ax+by+cz=d be written as f(x,y)=Ax+By+D?

Answer 1

By expressing z
In this case
z=(d-ax-by)/c
therefore
f(x,y)=(d-ax-by)/c

Answer 2

But how's that equal to Ax+By+D?

Answer 3

Well that's what it says so here: http://tutorial.math.lamar.edu/Classes/CalcIII/MultiVrbleFcns.aspx

Answer 4

\[f(x,y)=\frac{d-ax-by}{c}=\frac{-ax-by+d}{c}=\frac{-a}{c}x+\frac{-b}{c}y+\frac{d}{c}\]

\[=Ax+By+D\]

where \[A=\frac{-a}{c},B=\frac{-b}{c},D=\frac{d}{c}\]

Answer 5

Are there books or resources that show this same derivation as well? Particularly about the part saying that\[A=\frac{-a}{c}, B=\frac{-b}{c}, D=\frac d c\]