Before answering the question, I would like to present the different modes of persuasion, also referred to as ethical strategies or rhetorical appeals. They are maneuvers in rhetoric that classify the speaker's appeal to the audience. The Rhetorical Appeals are:
Ethos: It is how well the presenter convinces the audience that the presenter is qualified to speak on the subject, and by doing that what the presenter says is valid.
Pathos: is an appeal to the audience’s emotions
Logos: it. It is normally used to describe facts and figures that support the speaker's claims or thesis.
Kairos: An orator uses this to their advantage to persuade the audience to act now at the time being.
Even though you did not include the excerpt, I know for sure you mean this one:
<em>"She had told them about the place where they would stay, promising warmth and good food, holding these things out to them as an incentive to keep going."</em>
In this particular case the rhetoric appeal used is:
an appeal to the audience’s wants and needs which is a Pathos Rhetorical appeal.
