The answer

The points (1, 5) and (−3, 7) correspond to the POINTS (1, 5, 1) and (−3, 7, 1). Their LINE of intersection is (1, 5, 1) x (−3, 7, 1) = [−2, −4, 22]. In turn, this LINE is the plane −2x − 4y + 22z = 0, and so corresponds to the line −2x − 4y + 22 = 0.

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