https://file.aiquickdraw.com/mathbot/file/1726189967946b1xykqqc.jpg

The task in the image is to determine if a function is linear, and if it is, express it in the form \( f(x) = ax + b \). If the function is not linear, you are instructed to write "NO LINEAL".

### Given Functions:
1. The first function is \( f(x) = 7 - 6x \).
2. The second function is \( f(x) = \frac{-6}{x^2} \).

### Analysis:

1. **First Function: \( f(x) = 7 - 6x \)**  
   This is a linear function because it can be written in the form \( f(x) = ax + b \), where \( a = -6 \) and \( b = 7 \). Hence, it is linear.

2. **Second Function: \( f(x) = \frac{-6}{x^2} \)**  
   This function involves \( x^2 \) in the denominator, making it nonlinear. A linear function must have terms involving only \( x \) (raised to the first power) or constants, which this function does not satisfy. Therefore, this function is **not linear**.

### Conclusion:
- The first function \( f(x) = 7 - 6x \) is linear and can be expressed in the form \( f(x) = -6x + 7 \).
- The second function \( f(x) = \frac{-6}{x^2} \) is **not linear** (NO LINEAL).

Would you like further details or explanations? Here are some related questions you might want to explore:

1. What are the key properties of a linear function?
2. How do you differentiate between linear and nonlinear functions?
3. Can linear functions have more complex forms?
4. Why does the presence of \( x^2 \) make a function nonlinear?
5. How can we analyze a function's behavior graphically to identify linearity?

**Tip:** A function is linear if its graph is a straight line and if it can be expressed as \( f(x) = ax + b \), where \( a \) and \( b \) are constants.

Determine if the function is linear. If the function is linear, express the function in the form f(x) = ax + b. (If the function is not linear, write NO LINEAL.)

Learn how to determine if a function is linear and express it in the form f(x) = ax + b. Explore key algebraic concepts with examples including linear and nonlinear functions, suitable for students in Grades 9-11.

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