An equality constraint requires that only the points on the line described by the constraint are feasible.

Name: An equality constraint requires that only the points on the line described by the constraint are feasible.
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This is because an equality constraint sets the value of one variable equal to a constant value, making only the points on the line (or hyperplane in higher dimensions) feasible solutions. Points off the line will not satisfy the constraint and thus cannot be optimal solutions.

An Equality Constraint Requires That Only the Points on the Line