To determine whether the given function is linear, we can analyze its form and simplify it.

The function given is:

$f(x) = \frac{32 - x}{8}$

Let's simplify this function:

$f(x) = \frac{32}{8} - \frac{x}{8}$

Simplifying the fractions:

$f(x) = 4 - \frac{1}{8}x$

This function can be rewritten as:

$f(x) = -\frac{1}{8}x + 4$

This is in the form $f(x) = ax + b$, where $a = -\frac{1}{8}$ and $b = 4$.

Therefore, the function is linear and can be expressed as:

$f(x) = -\frac{1}{8}x + 4$

Would you like more details or have any questions? Here are some additional related questions:

1. What is the slope of the function $f(x) = -\frac{1}{8}x + 4$?
2. How would the graph of this function look like?
3. How does the value of $b$ affect the graph of the function?
4. What would the function look like if $b$ was zero?
5. How can we determine whether a function is linear or not just by looking at it?

Tip: In a linear function, the variable $x$ is always raised to the first power, and the function can be written in the form $ax + b$.