Practice worksheet for graphing linear equations with blank coordinate planes.

To solve this problem, we need to determine which of the given equations are linear. A linear equation is one that can be written in the form $Ax + By = C$, where $A$, $B$, and $C$ are constants, and $x$ and $y$ are variables. The key is that the variables $x$ and $y$ should not be raised to any power other than 1, and they should not be multiplied together or appear in any other complicated form.

Let's go through each equation step by step:

1. $y = 6$
- This equation can be rewritten as $0x + 1y = 6$. It fits the form $Ax + By = C$ with $A = 0$, $B = 1$, and $C = 6$. So, it is a linear equation.

2. $y^2 - 4x = 8$
- This equation has $y^2$, which means $y$ is raised to the power of 2. Therefore, it is not a linear equation.

3. $y = x^2 + 3$
- This equation has $x^2$, which means $x$ is raised to the power of 2. Therefore, it is not a linear equation.

4. $x + y = -2$
- This equation is already in the form $Ax + By = C$ with $A = 1$, $B = 1$, and $C = -2$. So, it is a linear equation.

5. $x^2 + y^2 = 4$
- This equation has both $x^2$ and $y^2$, which means both $x$ and $y$ are raised to the power of 2. Therefore, it is not a linear equation.

6. $5y - 3x = 12$
- This equation is already in the form $Ax + By = C$ with $A = -3$, $B = 5$, and $C = 12$. So, it is a linear equation.

Now, let's summarize the linear equations:
- $y = 6$
- $x + y = -2$
- $5y - 3x = 12$

The non-linear equations are:
- $y^2 - 4x = 8$
- $y = x^2 + 3$
- $x^2 + y^2 = 4$

Final Answer: The linear equations are $y = 6$, $x + y = -2$, and $5y - 3x = 12$.