John says the transformation rule (x, y) --> (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?

For this case we have the following transformation:
 (x, y) -> (x + 4, y + 7)
 The ordered pair to which the transformation is applied is:
 (x, y) = (4, 5)
 Therefore, applying the transformation we have:
 (4, 5) -> (4 + 4, 5 + 7) -----> (8, 12)
 The error for this case is that John made the following transformation:
 (4, 5) -> (4 - 4, 5 - 7) -----> (0, -2)
 That is, rest the numbers instead of adding.
 Answer:
 his error was subtract instead of adding.
 The correct answer is:
 (8, 12)