Answer:
b (2, 13)
Explanation:
In a function, no two ordered pairs can have the same x-coordinate.
The x-coordinates already listed are: -1, 0, 1.
Any ordered pair with one of those x-coordinates cannot be placed in the table for the relation to remain a function.
Choices c and d are out.
That leaves only choice a and b.
The relation is to remain a linear function.
Look at how a change in x results in a change in y.
In a linear function, equal changes in x must result in equal changes in y.
Points (-1, 4) and (0, 7)
From x = -1 to x = 0, the change in x is +1.
From y = 4 to y = 7, the change in y is +3.
Points (0, 7) and (1, 10)
From x = 0 to x = 1, the change in x is +1.
From y = 7 to y = 10, the change in y is +3.
Notice that in both cases, a change of +1 in x results in a change of +3 in y.
Both choices a and b have 2 as the x-coordinate.
Try choice b, (2, 13)
From (1, 10) to (2, 13), a change of +1 in x results in a change of +3 in y.
This is the same change we saw above in the other two sets of ordered pairs, so the answer is
b (2, 13)