To solve the equation $2x - 4y = 8$ for $y$, follow these steps:

1. Isolate the term with $y$: $2x - 4y = 8$ Subtract $2x$ from both sides: $-4y = 8 - 2x$

2. Divide each term by $-4$ to solve for $y$: $y = \frac{8 - 2x}{-4}$

3. Simplify the expression: $y = -\frac{8}{4} + \frac{2x}{4}$ $y = -2 + \frac{x}{2}$

Thus, the solution for $y$ is: $y = \frac{1}{2}x - 2$

Comparing this with the given choices in your image:

• $y = -2 + \frac{1}{2}x$

This corresponds to the correct choice.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you solve for $x$ in a linear equation with two variables?
2. What is the slope-intercept form of a linear equation?
3. How can you graph the equation $2x - 4y = 8$ on a coordinate plane?
4. What does the slope represent in the context of the equation $y = \frac{1}{2}x - 2$?
5. How do you verify if a point lies on the line represented by $2x - 4y = 8$?

Tip: Always double-check your algebraic manipulations to ensure accuracy when solving for a variable.