https://file.aiquickdraw.com/mathbot/file/1730513087474v4ugstt3.jpg

Let's solve for \( y \) in the equation:

\[
\frac{1}{2}x - 2y = -10
\]

### Step 1: Isolate the \( y \)-term
First, move the \(\frac{1}{2}x\) term to the other side by subtracting it from both sides:

\[
-2y = -\frac{1}{2}x - 10
\]

### Step 2: Divide by \(-2\) to solve for \( y \)
Now, divide every term by \(-2\):

\[
y = \frac{1}{4}x + 5
\]

### Answer
So, the solution is:

\[
y = \frac{1}{4}x + 5
\]

This matches the second option:
\[
\boxed{y = \frac{1}{4}x + 5}
\]

Would you like more details on any part of the solution? 

Here are some related questions to further your understanding:

1. How would you solve for \( x \) instead of \( y \) in this equation?
2. How does changing the coefficient of \( x \) affect the slope in the final solution?
3. What if we had a different constant term (e.g., \(-12\) instead of \(-10\))? How would the solution change?
4. How can you convert the equation to standard form after solving for \( y \)?
5. How does the sign of the coefficient of \( y \) impact the direction of the line?

**Tip:** When isolating variables, always perform the same operation on both sides of the equation to maintain equality.

Solve for y: \( \frac{1}{2}x - 2y = -10 \). Options: (A) \( y = -x - 5 \), (B) \( y = \frac{1}{4}x + 5 \), (C) \( y = x - 5 \), (D) \( y = -\frac{1}{4}x - 5 \)

Learn how to solve for y in the linear equation \( \frac{1}{2}x - 2y = -10 \). Follow a step-by-step solution to isolate y, resulting in the answer \( y = \frac{1}{4}x + 5 \). Perfect for students in Grades 8-10 covering linear equations and algebraic manipulation.

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