Answer:
C.
Explanation:
If equal changes in x result in equal changes in y, then the function is linear.
A. Are the changes from (2, 4) to (4, 1) and from (4, 1) to (6, 11) equal?
The change from (2, 4) to (4, 1):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -9 to 1; the change is 1 - (-9) = 10
The change from (4, 1) to (6, 11):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from 1 to 11; the change is 11 - 1 = 10
For a change in x of 2, the change in y is 10 in both cases. This function is linear.
B. Are the changes from (2, -14) to (4, -16) and from (4, -16) to (6, -18) equal?
The change from (2, -14) to (4, -16):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -14 to -16; the change is -16 - (-14) = -2
The change from (4, -16) to (6, -18):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from -16 to -18; the change is -18 - (-16) = -2
For a change in x of 2, the change in y is -2 in both cases. This function is linear.
C. Are the changes from (2, 0) to (4, 6) and from (4, 6) to (6, 16) equal?
The change from (2, 0) to (4, 6):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from 0 to 6; the change is 6 - 0 = 6
The change from (4, 6) to (6, 16):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from 6 to 16; the change is 16 - 6 = 10
For a change in x of 2, the change in y is 6 in one case and 10 in the other case. This function is not linear.
D. Are the changes from (2, -9) to (4, -6) and from (4, -6) to (6, -3) equal?
The change from (2, -9) to (4, -6):
When x changes from 2 to 4, the change is 4 - 2 = 2.
y changes from -9 to -6; the change is - 9 - (-6) = -3
The change from (4, -6) to (6, -3):
When x changes from 4 to 6, the change is 6 - 4 = 2.
y changes from -6 to -3; the change is -6 - (-3) = -3
For a change in x of 2, the change in y is -3 in both cases. This function is linear.