Definition: A function of the form
\[
z(x,y)=ax+by + c,
\]
where $a, b$ and $c$ are numbers such that not both $a$ and $b$ equal zero, is called a linear function of two variables.
Remark 1: For $a=b=0$ this is a constant function of two variables.
The graph of a linear function is a plane.
Example: The function $z(x,y) = 3 + x + y$ is an example of a linear function.
\[
z(x,y)=ax+by + c,
\]
where $a, b$ and $c$ are numbers such that not both $a$ and $b$ equal zero, is called a linear function of two variables.
Remark 1: For $a=b=0$ this is a constant function of two variables.
Example: The function $z(x,y) = 3 + x + y$ is an example of a linear function.