John says the transformation rule (x, y) to (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?

John's error is that he applied the transformation rule to the image instead to the pre-image.The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5). This results to (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image.