Final answer:
The correct ordered pairs that can be added to the set of points and still represent the same linear function are (2, -2) and (5, -11), as they maintain a consistent slope of -3, which is characteristic of the linear function described by the given points.
Step-by-step explanation:
The problem provided describes a set of ordered pairs that belong to a linear function, and the goal is to identify additional pairs that would still lie on the same line. To do this, we need to determine the slope (slope) of the linear function, which is the change in y divided by the change in x (often written as Δy/Δx). The slope should be consistent for all points on a straight line.
Looking at the given points, we can see that the change in the y-coordinate as the x-coordinate increases by 1 is consistent: from (-2,10) to (-1,7), y decreases by 3, and this pattern continues for the other points, yielding a slope of -3. Any additional points added to this function must have the same slope to maintain the linearity.
Now we can test the additional options:
- (2, -2): Starting from (1, 1) with x increasing by 1, y should decrease by 3, giving us (2, -2), which has a consistent slope of -3, so (2, -2) is on the same line.
- (5, -11): Starting from (1, 1) with x increasing by 4, y should decrease by 12 (4 times 3), giving us (5, -11), which also has a consistent slope of -3, so (5, -11) is on the same line.
The correct answers are thus choices A and C. Both these points maintain the slope of -3 relative to other points on the line.