Which set of ordered pairs $(x, y)$ could represent a linear function?
\[
\begin{array}{l}
\mathbf{A}=\{(-2,-1),(1,1),(4,2),(7,4)\} \\
\mathbf{B}=\{(-7,-7),(-3,-5),(3,-2),(7,0)\} \\
\mathbf{C}=\{(-2,-3),(0,0),(2,3),(5,6)\} \\
\mathbf{D}=\{(-6,2),(-2,1),(1,0),(4,-1)\}
\end{array}
\]
Answer

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 ：\(\boxed{\text{Therefore, set C could represent a linear function.}}\)