When using the reservation form, if we only want one person per time slot, will the time slots that are already reserved not show up? I don't want to

I'm trying to configure this for my reservation form.

If I can understand you correctly, you want your users to select only one option, if so, then this widget will be helpful: http://widgets.jotform.com/widget/appointment_slots. 

You may follow this guide, it will help you to add the widget to your form: http://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form.