We know that we are saved by Grace of Jesus Christ because the following Bible verses tell us so, and we believe the Bible to be the inspired Word of God:

Eph 2:8-9  For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast.

2Co_8:9  For you know the grace of our Lord Jesus Christ, that though he was rich, yet for your sake he became poor, so that you by his poverty might become rich.
Tit 2:11  For the grace of God has appeared, bringing salvation for all people.

Rom 3:21-24  But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus.

Romans Chapter 5 is especially good in explaining the philosophy of the atonement. I’m including only some of the verses below:

Rom. 5 Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ, 2 through whom also we have obtained our introduction by faith into this grace in which we stand… 8 But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us. 9 Much more then, having now been justified [e]by His blood, we shall be saved from the wrath of God through Him….12 Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned… 15 But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. 16 The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification. 17 For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.

In short – Adam sinned and from him an entire race of sinners was born – there was no one righteous that could give his life to die for Adam so that he and his race could live again. Therefore Jesus left the riches of heaven and was born as a man in order to give his life as a ransom (corresponding price) for Adam and his race. He offered his life freely and has opened a heavenly call for all those who want to follow on his footsteps now. These will have the opportunity to reign with Christ for 1000 years in order to bring the rest of mankind to perfection on earth, like God originally intended.

The Bible is clear that we are saved by grace, but we must work with the Holy Spirit to change our character for better and to produce the fruits of the spirit mentioned in Galatians 5:22-23. I will quote it here in the context:

Gal 5 16 But I say, walk by the Spirit, and you will not carry out the desire of the flesh. 17 For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please. 18 But if you are led by the Spirit, you are not under the Law. 19 Now the deeds of the flesh are evident, which are: immorality, impurity, sensuality, 20 idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, [j]factions, 21 envying, drunkenness, carousing, and things like these, of which I forewarn you, just as I have forewarned you, that those who practice such things will not inherit the kingdom of God. 22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such things there is no law. 24 Now those who [k]belong to Christ Jesus have crucified the flesh with its passions and desires.25 If we live by the Spirit, let us also [l]walk by the Spirit.