x 0 1 2 3 y 8 1 −6 −13 Is the relationship a linear function? How do you know? A. No; the change in x and the change in y is not constant. B. Yes; the change in x is constant and the change in y is not constant. C. Yes; the change in x is constant and the change in y is constant. D. No; the change in x is not constant and the change in y is constant.

The correct option is C) Yes; the change in x is constant and the change in y is constant.

Step-by-step explanation:

Consider the table shown.

x     y

0    8

1     1

2   -6

3   -13

Now observe the changes in x and y coordinates, if changes are constant then the given function is linear.

Consider the change in x coordinate.

1-0=1,  2-1=1 and 3-2=1

Now consider the change in y coordinate.

1-8=-7,  -6-1=-7  and -13-(-6)=-13+6=-7

Since the change in x and y is constant the given relationship is linear.

Therefore, the correct option is (C) Yes; the change in x is constant and the change in y is constant.