"Your horse is thirsty."
Translation:Dein Pferd hat Durst.
Dein is for nominative (masculine) which is the case of this sentence. You can check how to decline possessive pronouns as nouns and as adjetives in this page http://www.german-grammar.de/grammar/content/grammar_16_20.htm#chapter16
'Hat' is used because the horse HAS thirst as opposed to being physically being thirst. In German, 'ist' (is) isn't used unless the subject actually is that thing. For example, if the sentence was 'The horse is an animal' (Das Pferd ist ein Tier) you would say 'ist' because the horse IS an animal. In the case of the horse being thirsty through the mindset of German language, it is not actually thirsty, it merely has thirst.
ihr > Your (formal)
dein > your (singular familiar)
euer > y'all's (plural familiar)
Ihre, deine and euere are used for feminine and plural nouns.
Ihr Pferd hat Durst. > Your horse is thirsty.
Ihre Pferde haben Durst. > Your horses are thirsty.
Note that ihr(e) can also mean her and their; the difference is determined by context. Talking to someone: Ihr (capital) = Your
Talking about a woman: ihr = her
Talking about multiple people: ihr = their
Ihr can also be the pronoun "y'all."
Because Durst is a noun, not the adjective So the word by word translation of "The horse is thirsty" would be "das pferd ist durstig". You can say that in German as well. The direct translation of "das pferd hat durst" instead is "the horse has thirst". This is just the structure of saying things in german.
Where did you get the information that "dein" is synonymous with "du"? It is actually not, "du" means "you" (informal, singular), "dein" (possessive pronoun for "du") means "your". The subject is therefore [your] horse (3rd person singular), and the verb is therefore "hat" rather than "hast".
Maybe I should have said Dein is used for Du...I got this information from the table on the lesson for this section with the little light bulb. Since hast goes with du, and dein is used for du, why wouldn't it be Dein Pferd hast durst, OR Euer Pferd habt Durst since Euer is used for Ihr (Your) and habt goes with Ihr?
It is "Euer" and not "Eure" ,because Pferd is neutral ...if the sentence was "Your cat is thirsty" it would be "EURE Katze ist durstig" because Katze is feminine. Also Pferd is singular so if the sentence was "Your horses are thirsty" you could use "EURE Pferde (<- with e because of plural) sind durstig."
Yes, this is correct. The "Ihr" with capital "I" is used (like the englisch "your") in the plural the same as in the singular. It can be "you one's" or "you all's". But it gets a "e" at the end: "Ihre: if the following noun has the article "die": "die Tochter" (daughter) - "Ihre Tochter hat Durst." Plural: "die Pferde" - "Ihre Pferde haben Durst." Adult people prefer this formal "Ihr". But related persons and friends say: dein(e) and to several persons: "euer" and if the following noun has the article "die": "eure".