To express the equation \(2x - 4y = 8\) in the form \(y = mx + b\), follow these steps:

1. Start with the given equation:
   \[
   2x - 4y = 8
   \]

2. Subtract \(2x\) from both sides to isolate the term involving \(y\):
   \[
   -4y = -2x + 8
   \]

3. Divide the entire equation by \(-4\) to solve for \(y\):
   \[
   y = \frac{-2x}{-4} + \frac{8}{-4}
   \]

4. Simplify the equation:
   \[
   y = \frac{1}{2}x - 2
   \]

So, the equation in the form \(y = mx + b\) is:
\[
y = \frac{1}{2}x - 2
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you determine the slope \(m\) and the y-intercept \(b\) from the equation \(y = mx + b\)?
2. Can you graph the equation \(y = \frac{1}{2}x - 2\) and identify the slope and y-intercept on the graph?
3. What is the significance of the slope and y-intercept in the context of a linear equation?
4. How would you convert a different linear equation, like \(3x + 6y = 12\), into the slope-intercept form?
5. How can the slope \(m\) help determine if two lines are parallel or perpendicular?

**Tip:** The slope \(m\) represents the steepness of the line, and the y-intercept \(b\) is where the line crosses the y-axis.

Discover how to convert the linear equation 2x - 4y = 8 into the slope-intercept form y = mx + b with this step-by-step guide. This problem emphasizes algebraic manipulation and understanding the properties of linear equations, ideal for students in Grades 8-10.

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