https://file.aiquickdraw.com/mathbot/file/172683736748430k9u76n.jpg

Let's analyze the equations and determine whether they represent linear or nonlinear functions:

1. **\( y = 2x - 9 \)**:
   - This is a linear equation since it is in the form \( y = mx + b \), where \( m \) and \( b \) are constants.
   - **Linear**

2. **\( y = \frac{5}{x} \)**:
   - This is a nonlinear equation because it involves a variable in the denominator.
   - **Nonlinear**

3. **\( y = 3x^2 \)**:
   - This is a nonlinear equation because it contains a square term (\( x^2 \)).
   - **Nonlinear**

4. **\( 4x + y = 7 \)**:
   - This is a linear equation because it can be rearranged into the form \( y = -4x + 7 \), which is linear.
   - **Linear**

5. **\( y = \frac{1}{2} \)**:
   - This is a linear equation, as \( y \) is constant and doesn't depend on \( x \).
   - **Linear**

6. **\( y = \sqrt{x + 3} \)**:
   - This is a nonlinear equation because it involves a square root of a variable.
   - **Nonlinear**

### Final Classification:
1. \( y = 2x - 9 \): **Linear**
2. \( y = \frac{5}{x} \): **Nonlinear**
3. \( y = 3x^2 \): **Nonlinear**
4. \( 4x + y = 7 \): **Linear**
5. \( y = \frac{1}{2} \): **Linear**
6. \( y = \sqrt{x + 3} \): **Nonlinear**

Would you like more details on any of these classifications? Here are 5 related questions to explore further:

1. What are the characteristics of a linear function?
2. How do nonlinear functions differ from linear ones?
3. Can an equation with exponents of \( x \) greater than 1 ever be linear?
4. How do you graph linear and nonlinear equations?
5. What types of real-world phenomena are modeled by nonlinear functions?

**Tip**: Linear equations have a constant rate of change, while nonlinear ones often show variable rates of change.

Indicate whether each equation represents a linear or nonlinear function.

Learn how to identify whether an equation is linear or nonlinear. This guide covers key algebraic concepts such as linear equations (y = mx + b) and nonlinear functions like square root and quadratic equations. Suitable for students in Grades 7-9.

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