Rom 1:17

1:17 righteousness of God. This is a key phrase in Romans (3:21; 5:19; 10:3), regularly explained in the letter as “righteousness . . . through (or of) faith” (3:22; cf. 9:30; 10:6). God’s righteousness is shown in the righteousness of Christ that is imputed to, or considered by God to belong to, the one who believes. This imputation of righteousness to sinners who believe is fully consistent with the personal righteousness of God. As a just and righteous judge (2:5–16), God through the death of His Son justifies, or declares righteous, those sinners who come to true faith in Christ (3:21–26; 5:10). Luther’s reading of this verse had a decisive impact on his understanding of justification.

from faith for faith. Paul emphasizes that at every point of its influence the gospel depends on faith, not works.

as it is written. Hab. 2:4 provides the biblical basis for and summary of what follows, indicating that the way of life by faith was already known in the Old Testament.

shall live. Life in contrast with spiritual death, and life in the sense of continuing in fellowship with God. From first to last, godly living means trusting in God and depending on His grace.