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To rewrite the equation \( 2x - 4y = -16 \) into slope-intercept form (\( y = mx + b \)), follow these steps:

### Step-by-Step Solution:
1. Start with the given equation:
   \[
   2x - 4y = -16
   \]

2. Isolate the \( y \)-term by subtracting \( 2x \) from both sides:
   \[
   -4y = -2x - 16
   \]

3. Solve for \( y \) by dividing everything by \( -4 \):
   \[
   y = \frac{-2x - 16}{-4}
   \]

4. Simplify the fractions:
   \[
   y = \frac{-2x}{-4} + \frac{-16}{-4}
   \]
   This becomes:
   \[
   y = \frac{1}{2}x + 4
   \]

### Final Answer:
The slope-intercept form of the equation is:
\[
y = \frac{1}{2}x + 4
\]

In this form, the slope (\( m \)) is \( \frac{1}{2} \) and the y-intercept (\( b \)) is \( 4 \).

Would you like more details or have any questions about this? 

Here are five related questions for further exploration:
1. What is the slope of the line, and how do you interpret it?
2. How do you graph a line using the slope-intercept form?
3. What are parallel lines, and how can you use the slope to identify them?
4. How would you find the equation of a line passing through a specific point and having the same slope?
5. Can you convert this equation into standard form again after converting it to slope-intercept form?

**Tip:** When simplifying fractions, always check if both terms share a common factor to simplify efficiently.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 2x - 4y = -16

Learn how to convert the linear equation 2x - 4y = -16 into slope-intercept form with step-by-step explanations. This problem explores key algebra concepts, such as solving for y and simplifying fractions, suitable for students in Grades 8-10.

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