We affirm the crucial doctrine of the sinlessness of Christ. If Jesus sinned, He could no longer be our sin-bearer. The question remains, though Jesus was specifically tested (tempted) in Luke 4, was He actually capable of sinning? The formal term in the affirmative answer to this question is peccability, while impeccability states that Jesus was not capable of sinning. At the crux of the discussion is relationship between the divine and human nature of Jesus. Godly pastors and theologians have disagreed on this specific question, a reflection of how nuanced it is with its many implications.
This is a deep study, I welcome your input! I personally favor Walvoord's perspective at this time. Feel free to email with comments.