Jacob is the positive example of God’s special intervention in the life of one man to insure His purpose. Pharaoh is the negative example.
It is clear from the Hebrew that God’s interaction with Pharaoh through Moses is the precedent for Pharaoh’s hardened heart, but it was Pharaoh that hardened his own heart. He refused to repent of unbelief and the trust he had in his false gods and trust in the God of Israel. That unwillingness to repent with each new plague only hardened his heart further and further as the ordeal progressed. The Theological Workbook of the Old Testament (Volume I by Harris, Archer and Waltke; Moody Press) states regarding the Hebrew word chazaq (khaw-zak’), translated “hardened” in Exodus 12:12:“The hardening of Pharaoh’s heart is an old problem, one that is more theological than linguistic. The verb hazag is used twelve times in the narrative (Ex 4-14), mostly with the Lord as the agent (“Pharaoh’s heart was hardened”). Also, the verb kabed is used five times, both with the Lord as the agent, with Pharaoh as the agent, and in the passive sense. The verb qasha is used once with the Lord as the agent. There is no discernable difference here in the usage of these words. It is clear that Pharaoh was an unrepentant sinner at the start (chapter 5). It is perhaps enough to point this out and remark that all of God’s hardening of an obstinate sinner was judicial and done that God’s deliverance should be the more memorable. And this, too, was in God’s plan (Ex 9:16), though it is also inexplicably true that Pharaoh sinned freely and was therefore terribly guilty (cf. Acts 4:25-28).” (Statement by R. L. Harris)
God’s plagues were primarily against the idols of Egypt in proving them false. The Egyptian Pharaohs believed they were offspring of their gods. Therefore, for Pharaoh to accept the God of Israel as the only God, he would have to reject his own claim to deity and his right/authority to hold the position of Pharaoh. He had a lot of incentive to reject the God of Israel. We can find a parallel and comparison in Romans 1:19-32 to what took place in God’s dealing with Pharaoh in that God deals similarly with all unbelievers as they resist His revelation of Himself and as they refuse to repent of their unbelief. It was Pharaoh’s own unbelief and refusal to repent that hardened his heart. To reject God in unbelief is actually an act of self-deification (just like Pharaoh). “Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things. Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves: Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen. For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature: And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet. And even as they did not like to retain God in their knowledge, God gave them over to a reprobate mind, to do those things which are not convenient” (Romans 1:22-28; compare Romans 2:4-5).