Question 1021609
A linear equation in one independent variable can be shown as a 2D line. 
Example : {{{y=2x+1}}} is a line with slope of 2 and a y-intercept of 1.
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A linear equation in two independent variables can be shown as a 3D plane.
Example : {{{z=3x-4y+10}}} is a plane with a normal vector (-3,4,1).
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So the additional variable adds an additional dimension.
Adding a third variable would make a 4D hyperplane which is more difficult to visualize but it's the same as going from 2D to 3D, now you go from 3D to 4D and so on.