Apologies if this is in the wrong section.

I've always been stumped by multi variable functions as seen in economics:

Use of Functions and Variables in Economics

If you have one variable, you get a linear function. If that variable has a power, then it's non linear.

I don't understand why having multiple variables for example all to the power of one... yields a line?

Doesn't the addition of more variables turn the graph into a multi dimensional one? Is this even related to multivariate calculus?