To find the answer, we turn to the Bible (Genesis 21:5-21), the Koran and other sources.
In Genesis, when Abraham send Hagar and Ishmael away (at Sarah's insistence) God promised to make Hagar's son the father of a great nation. (See Genesis 21:13 & 18) Although there appeared to be virtually no chance that Hagar and Ishmael could survive in the Negev Desert, Abraham still provided Hagar with provisions. This was a sign of his protection of Hagar and his firstborn, a sign that they should not be harmed. We later see how God came to Hagar, giving her His protection and providing water to her and Ishmael.
Birthright of Abraham
The Book of Genesis also tells us how the blessing (birthright) of Abraham was given to Isaac, Abraham's son by his wife Sarah.
The Koran gives a very different story. Hagar is not mentioned by name in the Koran, but the mother of Ishmael is prominent. Women are seldom mentioned by name in the Koran, so this would not be unusual.
In the Koran, it is Ishmael, not Isaac, who received the birthright of Abraham. The Koran also says that it was Ishmael, not Isaac, who was to be sacrificed to God. These two fundamental differences have been extremely important throughout history and are one major source of the differences between Arabs (Muslims) and Jews today.
The Genealogy of Muhammad
Abraham - Hagar
Ishmael -- Egyptian Wife
Kedar and all Arabs
Prophet of Islam
Ismael, Prophet of Islam
In the Koran, Abraham joins Ishmael in what is now called Mecca (in Saudi Arabia). There they rebuilt an altar to God that was first built by Adam and destroyed in Noah's Flood. This is also the site where Hagar found a well as mention in Genesis.
In the Koran (19:54), Ishmael is described as a messenger and prophet. In Islam, it was Ishmael who was to be sacrificed, received the birthright of Abraham, founded the city known as Mecca and was an ancestor of the Prophet Muhammad.