* REQUIRED 9. If a function $f$ has values $f(5)=12$ and $f(10)=18$, use what you have learned about filnction patterns to find $f(20)$ if $f$ is a linear function. \[ f(20)= \]

Step 1 ：The function is a linear function, which means it follows the pattern of \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：Given two points \((5,12)\) and \((10,18)\), we can calculate the slope \(m\) as \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 12}{10 - 5} = \frac{6}{5} = 1.2\).

Step 3 ：Then we can substitute one of the points into the equation to solve for \(b\). Let's use the point \((5,12)\), so \(12 = 1.2*5 + b\), which gives \(b = 12 - 6 = 6\).

Step 4 ：So the function is \(f(x) = 1.2x + 6\). We can substitute \(x = 20\) into the function to find \(f(20)\).

Step 5 ：\(f(20) = 30.0\)

Step 6 ：Final Answer: \(\boxed{30.0}\)