Paul's Online Notes
Paul's Online Notes
Home / Calculus III / 3-Dimensional Space / The 3-D Coordinate System
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 12.1 : The 3-D Coordinate System

4. List all of the coordinates systems (\(\mathbb{R}\), \({\mathbb{R}^2}\), \({\mathbb{R}^3}\)) that the following equation will have a graph in. Do not sketch the graph.

\[7{x^2} - 9{y^3} = 3x + 1\] Show Solution

First notice that because there are two variables in this equation it cannot have a graph in \(\mathbb{R}\) since equations in that coordinate system can only have a single variable.

There are two variables in the equation so we know that it will have a graph in \({\mathbb{R}^2}\).

Likewise, the fact that the equation has two variables means that it will also have a graph in \({\mathbb{R}^3}\). Although in this case the third variable, \(z\), can have any value.