The question in the image is asking for the equation $x + 2y = 14$ to be solved for $y$. Let's isolate $y$ in the equation:

Starting with the equation: $x + 2y = 14$

1. Subtract $x$ from both sides: $2y = -x + 14$

2. Now divide both sides by 2 to solve for $y$: $y = \frac{-x + 14}{2}$

Simplifying the expression: $y = -\frac{1}{2}x + 7$

So, the correct answer is D: $y = -\frac{1}{2}x + 7$.

Would you like more details on this, or is there anything else you'd like to explore? Here are some related questions to help expand your understanding:

1. How would you solve an equation like $2x + 3y = 12$ for $y$?
2. What is the difference between solving for $y$ and solving for $x$?
3. How can you check the solution you derived from an equation?
4. How do you handle equations with more complex variables when solving for one of them?
5. What are the key properties of a linear equation when written in slope-intercept form?

Tip: When solving linear equations for a variable, always aim to isolate the variable on one side of the equation and simplify as much as possible!