vue.js Property or method is not defined

The data is not added to the table because basically, you are adding empty properties in addNewItem method.

addNewItem() {
    this.items.push({
        id: '',
        age: '',
        first_name: '',
        last_name: ''
     });
 }

The items list variable is where you are going to insert all your items. For the form data, you should create another variable to catch them and then push the single object to the list:

export default{
    data(){
        return{
            // single object where you are going to catch form data
            item:{
              id: null,
              age: null,
              first_name: '',
              last_name: ''
            }

            // Your list of objects
            items: [
              { id: 1, age: 40, first_name: 'Dickerson', last_name: 'Macdonald'},
              { id: 2, age: 21, first_name: 'Larsen', last_name: 'Shaw' },
              { id: 3, age: 89, first_name: 'Geneva', last_name: 'Wilson' },
              { id: 4, age: 38, first_name: 'Jami', last_name: 'Carney' }
            ],
        }
    }
}

so, in the input models instead of items.property_name use item.property_name

<b-form inline>
    <b-form-input
        v-model="item.id"
        requierd
        placeholder="Id"
    ></b-form-input>
    <b-form-input
        v-model="item.age"
        requierd
        placeholder="Age"
    ></b-form-input>
    <b-form-input
        v-model="item.first_name"
        requierd
        placeholder="First Name"
     ></b-form-input>
     <b-form-input
        v-model="item.last_name"
        requierd
        placeholder="Last Name"
     ></b-form-input>
   </b-form>

then in the addNewItem() Method push the single object to the list

addNewItem() {
    this.items.push(this.item);
 }