A family of Microsoft relational database management systems designed for ease of use.
In addition to designating a primary key for the animals 3 table and referencing this by a foreign key column in Slides 1, I would recommend that the relationship between the two tables then be enforced by selecting 'Enforce referential integrity' in the edit relationship dialogue. If Access does not allow you to do this, it would indicate that there is at least one row in Slides 1 without a match in animals 3.
Not directly connected to your current issue, but I would point out that Slides 1 is not normalized to Third Normal Form by virtue of the inclusion of City, State/Province, and Country columns. This leaves the table open to the risk of update anomalies. The table should include a numeric CityID foreign key column referencing the autonumber. primary key of a Cities table. City names cannot be used as a key as these can legitimately be duplicated. The Cities table should then include a foreign key referencing the primary key of a States_Provinces table, which should include a foreign key referencing the primary key of a Countries table.
You might like to take a look at DatabaseBasics.zip in my Dropbox public databases folder at:
This little demo file illustrates, amongst other things, such a correctly normalized set of tables. The option for 'Inserting data via a form/subforms' opens a form in which data can be inserted using correlated combo boxes, by selecting a country, then a region and then a city, with option at each level of the hierarchy to insert a new value not currently represented in the database.
Decomposing the table into s et of predefined related tables can be done by means of a set of 'append' queries. The DemposerDemo.zip file in the same Dropbox folder illustrates this, using non-normalized data imported from Excel.