Final answer:
The two ordered pairs that can be added to the given set and still have the set represent the same linear function are Option B. (5, -11) and Option D. (2, -2).
Step-by-step explanation:
A linear function rule is represented by the ordered pairings (-2, 10), (-1, 7), (0, 4), and (1, 1). We may look at the pattern of the supplied pairings to find two more ordered pairs that still represent the same linear function. The x-coordinate rises by 1 and the y-coordinate falls by 3 in each pair. As a result, we must locate two pairs that share the same pattern.
Option A. (5, 1) does not fit the pattern found in the pairs that are provided. Instead of increasing by 1, the x-coordinate grows by 4. Option B. (5, -11) adheres to the pattern found in the pairs provided. One is added to the x-coordinate, and three is subtracted from the y-coordinate. As a result, the linear function represented by this pair remains unchanged when it is added to the existing set. Option C. (-3, 15) does not fit the pattern found in the pairs that are provided. Instead of increasing by 1, the x-coordinate falls by 1. Option D. (2, -2) adheres to the pattern found in the pairs that are provided. One is added to the x-coordinate, and three is subtracted from the y-coordinate. Therefore, this pair can be added to the given set and still represent the same linear function. Option E. (3, -1) does not follow the pattern observed in the given pairs. The x-coordinate should increase by 1, but it increases by 2 instead.
Therefore, the two ordered pairs that can be added to the given set and still have the set represent the same linear function are Option B. (5, -11) and Option D. (2, -2).