Determine whether the given function is linear. If the function is linear, express the function in the form 
f(x) = ax + b.
 (If the function is not linear, enter NOT LINEAR.)
f(x) = 
32 − x
8


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 \( ax + b \).

Determine whether the given function is linear. If the function is linear, express the function in the form f(x) = ax + b. (If the function is not linear, enter NOT LINEAR.) f(x) = (32 − x)/8

Explore how to determine if the function f(x) = (32 − x)/8 is linear. This problem explains how to express the function in the form f(x) = ax + b. Step-by-step solution provided for algebraic concepts. Suitable for Grades 8-10.

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