"Chapter 83—The Walk to Emmaus This chapter is based on Luke 24:13-33 . Late in the afternoon of the day of the resurrection, two of the disciples were on their way to Emmaus, a little town eight miles from Jerusalem. These disciples had had no prominent place in Christ's work, but they were earnest believers in Him. They had come to the city to keep the Passover, and were greatly perplexed by the events that had recently taken place. They had heard the news of the morning in regard to the removal of Christ's body from the tomb, and also the report of the women who had seen the angels and had met Jesus. They were now returning to their homes to meditate and pray. Sadly they pursued their evening walk, talking over the scenes of the trial and the crucifixion. Never before had they been so utterly disheartened. Hopeless and faithless, they were walking in the shadow of the cross. DA 795"
"And, behold, two of them went that same day to a village called Emmaus, which was from Jerusalem about threescore furlongs. And they talked together of all these things which had happened. And it came to pass, that, while they communed together and reasoned, Jesus himself drew near, and went with them. But their eyes were holden that they should not know him. And he said unto them, What manner of communications are these that ye have one to another, as ye walk, and are sad? And the one of them, whose name was Cleopas, answering said unto him, Art thou only a stranger in Jerusalem, and hast not known the things which are come to pass there in these days? And he said unto them, What things? And they said unto him, Concerning Jesus of Nazareth, which was a prophet mighty in deed and word before God and all the people: And how the chief priests and our rulers delivered him to be condemned to death, and have crucified him. But we trusted that it had been he which should have redeemed Israel: and beside all this, to day is the third day since these things were done. Yea, and certain women also of our company made us astonished, which were early at the sepulchre; And when they found not his body, they came, saying, that they had also seen a vision of angels, which said that he was alive. And certain of them which were with us went to the sepulchre, and found it even so as the women had said: but him they saw not. Then he said unto them, O fools, and slow of heart to believe all that the prophets have spoken: Ought not Christ to have suffered these things, and to enter into his glory? And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself. And they drew nigh unto the village, whither they went: and he made as though he would have gone further. But they constrained him, saying, Abide with us: for it is toward evening, and the day is far spent. And he went in to tarry with them. And it came to pass, as he sat at meat with them, he took bread, and blessed it, and brake, and gave to them. And their eyes were opened, and they knew him; and he vanished out of their sight. And they said one to another, Did not our heart burn within us, while he talked with us by the way, and while he opened to us the scriptures?"
EGW explicitly states that the chapter is based on Luke 24:13-33 and retells the story with commentary.
"They had not advanced far on their journey when they were joined by a stranger, but they were so absorbed in their gloom and disappointment that they did not observe him closely. They continued their conversation, expressing the thoughts of their hearts. They were reasoning in regard to the lessons that Christ had given, which they seemed unable to comprehend. As they talked of the events that had taken place, Jesus longed to comfort them. He had seen their grief; He understood the conflicting, perplexing ideas that brought to their minds the thought, Can this Man, who suffered Himself to be so humiliated, be the Christ? Their grief could not be restrained, and they wept. Jesus knew that their hearts were bound up with Him in love, and He longed to wipe away their tears, and fill them with joy and gladness. But He must first give them lessons they would never forget. DA 795.2"
"And it came to pass, that, while they communed together and reasoned, Jesus himself drew near, and went with them."
The EGW passage directly recounts the story in Luke 24, and the verse cited is a key element of that story. The EGW passage amplifies the narrative, adding details about the emotions and thoughts of the disciples, but it is clearly based on the biblical account.
"After that he appeared in another form unto two of them, as they walked, and went into the country."
Both passages refer to Jesus appearing to two disciples on a journey. While the details differ (Luke 24 is the road to Emmaus, Mark 16 is more general), the core theme of a post-resurrection appearance to traveling disciples connects them.