Find the linear function with the following properties.
\[
\begin{array}{c}
f(-5)=6 \\
f(-6)=-9
\end{array}
\]
Answer
\[
f(x)=
\]

Step 1 ：Given two points (-5,6) and (-6,-9) on the line, we can find the slope (m) using the formula \(m = \frac{y2 - y1}{x2 - x1}\).

Step 2 ：Substituting the given points into the formula, we get \(m = \frac{-9 - 6}{-6 - (-5)} = 15.0\).

Step 3 ：Now that we have the slope, we can find the y-intercept (b) using the point-slope form of a line, which is \(y - y1 = m(x - x1)\).

Step 4 ：Substituting the slope and one of the given points into the formula, we get \(6 = 15(-5) + b\), which simplifies to \(b = 81.0\).

Step 5 ：Finally, we can write the equation of the line in slope-intercept form, which is \(y = mx + b\).

Step 6 ：Substituting the slope and y-intercept into the formula, we get \(f(x) = 15x + 81\).

Step 7 ：\(\boxed{f(x) = 15x + 81}\) is the final answer.