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To rewrite the given equation as a function of \( x \), let's start with the equation provided:

\[
-6x^2 + x + 5y = -6y
\]

### Step-by-Step Solution

1. **Move all terms involving \( y \) to one side**:
   \[
   -6x^2 + x + 5y + 6y = 0
   \]
   Simplify by combining like terms:
   \[
   -6x^2 + x + 11y = 0
   \]

2. **Isolate \( y \) in terms of \( x \)**:
   \[
   11y = 6x^2 - x
   \]

3. **Divide by 11 to solve for \( y \)**:
   \[
   y = \frac{6x^2 - x}{11}
   \]

### Final Answer
The equation rewritten as a function of \( x \) is:
\[
y = \frac{6x^2 - x}{11}
\]

Would you like further details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would you rewrite the equation as a function of \( y \) instead?
2. How can you determine if this function is one-to-one?
3. What is the domain of \( y = \frac{6x^2 - x}{11} \)?
4. How does changing the coefficient of \( x^2 \) affect the graph of the function?
5. Can you find the points where this function intersects the \( y \)-axis?

**Tip:** When rewriting relations as functions, always isolate the dependent variable on one side of the equation.

Learn how to rewrite the equation -6x^2 + x + 5y = -6y as a function of x. This step-by-step solution includes isolating variables and simplifying terms, helping students understand function creation from algebraic relations.

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