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### Section 1-1 : The 3-D Coordinate System

5. 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.

${x^3} + \sqrt {{y^2} + 1} - 6z = 2$ Show Solution

This equation has three variables and so it will have a graph in $${\mathbb{R}^3}$$.

On other hand because the equation has three variables in it there will be no graph in $${\mathbb{R}^2}$$(can have at most two variables) and it will not have a graph in $$\mathbb{R}$$ (can only have a single variable).