Answer:
C.
Step-by-step 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?
<u>The change from (2, 4) to (4, 1):</u>
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
<u>The change from (4, 1) to (6, 11):</u>
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?
<u>The change from (2, -14) to (4, -16):</u>
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
<u>The change from (4, -16) to (6, -18):</u>
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?
<u>The change from (2, 0) to (4, 6):</u>
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
<u>The change from (4, 6) to (6, 16):</u>
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?
<u>The change from (2, -9) to (4, -6):</u>
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
<u>The change from (4, -6) to (6, -3):</u>
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.
