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.