Let [Formula: see text] be integers and [Formula: see text] be any prime power [Formula: see text] such that [Formula: see text]. We say that the extension [Formula: see text] possesses the line property for [Formula: see text]-primitive elements if, for every [Formula: see text], such that [Formula: see text], there exists some [Formula: see text], such that [Formula: see text] has multiplicative order [Formula: see text]. Likewise, if, in the above definition, [Formula: see text] is restricted to the value [Formula: see text], we say that [Formula: see text] possesses the translate property. In this paper, we take [Formula: see text] (so that necessarily [Formula: see text] is odd) and prove that [Formula: see text] possesses the translate property for 2-primitive elements unless [Formula: see text]. With some additional theoretical and computational effort, we show also that [Formula: see text] possesses the line property for 2-primitive elements unless [Formula: see text].