Decide whether the following table represents a linear or quadratic function. Once you decide which it is, find $b-a$. \begin{tabular}{|c|c|c|c|c|c|c|} \hline$x$ & -2 & 0 & 4 & 6 & 7 & 8 \\ \hline$y$ & -8 & -5 & 1 & 4 & $a$ & $b$ \\ \hline \end{tabular}

Step 1 ：Calculate the rate of change between the first two points and the second two points: \(\frac{-5 - (-8)}{0 - (-2)} = 1.5\) and \(\frac{1 - (-5)}{4 - 0} = 1.5\)

Step 2 ：Since the rate of change is constant, the function is linear.

Step 3 ：Use the slope 1.5 and the point (0,-5) to find the equation of the line: \(y = 1.5x - 5\)

Step 4 ：Substitute \(x = 7\) into the equation to find a: \(a = 1.5*7 - 5 = 5.5\)

Step 5 ：Substitute \(x = 8\) into the equation to find b: \(b = 1.5*8 - 5 = 7\)

Step 6 ：Finally, find \(b - a = 7 - 5.5 = 1.5\)

Step 7 ：\(\boxed{1.5}\) is the final answer.