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
Equation 9 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.