Find the slope (rate of change) for each function:

• A: $g(x) = 6$ is a constant function. Slope $= 0$.
• B: $g(x) = 8x + 7$ is linear with slope $= 8$.
• C: Line through $(0, 6)$ and $(3, 0)$: slope $= \frac{0 - 6}{3 - 0} = -2$.
• D: Line through $(-6, 0)$ and $(4, 5)$: slope $= \frac{5 - 0}{4 - (-6)} = \frac{5}{10} = \frac{1}{2}$.
• E: From the graph, the line passes through $(-1, 1)$ and $(0, 5)$: slope $= \frac{5 - 1}{0 - (-1)} = 4$.

The greatest rate of change is $8$, which belongs to B: $g(x) = 8x + 7$.