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To solve the given equation and justify each step, we can break it down as follows:

### Equation:
\[
\frac{1}{2}x - \frac{3}{4}y = -2
\]

### Step 1: Isolate the \(y\)-term
Use the **Subtraction Property of Equality** to move \(\frac{1}{2}x\) to the right-hand side by subtracting it from both sides.

\[
-\frac{3}{4}y = -2 - \frac{1}{2}x
\]
Explanation: Subtract \(\frac{1}{2}x\) from both sides.
Reason: Subtraction Property of Equality.

### Step 2: Solve for \(y\)
Now, use the **Multiplication Property of Equality** to eliminate the fraction. Multiply both sides of the equation by \(-\frac{4}{3}\) (the reciprocal of \(-\frac{3}{4}\)) to solve for \(y\).

\[
y = \left(-2 - \frac{1}{2}x\right) \times -\frac{4}{3}
\]
Explanation: Multiply both sides by \(-\frac{4}{3}\).
Reason: Multiplication Property of Equality.

This is the solution to the equation, and each step has been justified using algebraic properties.

Would you like me to expand further or explain more details? Here are some relative questions for deeper exploration:

1. Why is multiplying by the reciprocal of a fraction necessary to isolate a variable?
2. What happens if we had a different sign in front of \(\frac{3}{4}y\)?
3. Can you explain how the properties of equality allow for balancing equations?
4. How does this process change when dealing with decimals instead of fractions?
5. What are the implications of negative signs when isolating terms?

**Tip**: Always check your solution by substituting it back into the original equation!

Solve the equation for y. Justify each step. 1/2x - 3/4y = -2.

Learn how to solve the linear equation 1/2x - 3/4y = -2 by isolating the variable y. This detailed step-by-step solution covers key algebraic concepts, including the use of the Subtraction and Multiplication Property of Equality. Suitable for students in Grades 7-10.

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