Step 1 :Calculate the slope between the first two points in each set:
Step 2 :\(A: \frac{1-(-1)}{1-(-2)} = \frac{2}{3}\)
Step 3 :\(B: \frac{-5-(-7)}{-3-(-7)} = \frac{2}{4} = \frac{1}{2}\)
Step 4 :\(C: \frac{0-(-3)}{0-(-2)} = \frac{3}{2}\)
Step 5 :\(D: \frac{1-2}{-2-(-6)} = \frac{-1}{4}\)
Step 6 :Calculate the slope between the second and third points in each set:
Step 7 :\(A: \frac{2-1}{4-1} = \frac{1}{3}\)
Step 8 :\(B: \frac{-2-(-5)}{3-(-3)} = \frac{3}{6} = \frac{1}{2}\)
Step 9 :\(C: \frac{3-0}{2-0} = \frac{3}{2}\)
Step 10 :\(D: \frac{0-1}{1-(-2)} = \frac{-1}{3}\)
Step 11 :Only set C has a constant slope between the first two points and the second two points.
Step 12 :\(\boxed{\text{Therefore, set C could represent a linear function.}}\)