The solution space of a single
equality constraint
We start our investigation regarding the geometrical representation of 2-var
linear constraints by considering first constraints of the equality type, i.e.,
It is a well-known result that, assuming
, this equation corresponds to a straight line with slope
and intercept
. In the special case where
, the solution space (locus) of Equation9
is still a straight line perpendicular to the
-axis, intersecting it at the point
. Notice that the presence of an equality constraint restricts the
dimensionality of the feasible solution space by one degree of freedom, i.e., it
turns it from a planar area to a line segment.
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