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The question asks for the key features of the equation \(2x + 4y = 8\) that can be used to sketch a graph, particularly focusing on the \(x\)-intercept, \(y\)-intercept, and slope. Let's break this down.

1. **Rewrite the equation in slope-intercept form \(y = mx + b\):**

   Start with the given equation:
   \[
   2x + 4y = 8
   \]

   Solve for \(y\):

   \[
   4y = -2x + 8
   \]

   Divide by 4:

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

   Now we can see that the slope (\(m\)) is \(-\frac{1}{2}\) and the \(y\)-intercept (\(b\)) is \(2\).

2. **Find the \(x\)-intercept:**

   To find the \(x\)-intercept, set \(y = 0\) in the original equation:

   \[
   2x + 4(0) = 8 \quad \Rightarrow \quad 2x = 8 \quad \Rightarrow \quad x = 4
   \]

   So, the \(x\)-intercept is \(4\).

3. **Key features:**
   - \(x\)-intercept: \( (4, 0) \)
   - \(y\)-intercept: \( (0, 2) \)
   - Slope: \(-\frac{1}{2}\)

Thus, the correct answer is the second option: 
**\(x\)-intercept (4, 0), \(y\)-intercept (0, 2), and slope \(m = -\frac{1}{2}\)**.

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Would you like more details or explanations about this? Here are some follow-up questions:

1. How do you find the slope from a general equation?
2. Why is it important to convert the equation to slope-intercept form?
3. Can you explain how the intercepts help sketch the graph of a line?
4. What is the significance of a negative slope?
5. How do you determine the intercepts of a line from the standard form?

**Tip:** Always try to convert equations to slope-intercept form \(y = mx + b\) when you need to quickly determine the slope and intercepts!

What are the key features of 2x + 4y = 8 that can be used to sketch a graph?

Learn how to identify the x-intercept, y-intercept, and slope from the linear equation 2x + 4y = 8. This problem covers key concepts in graphing linear equations, suitable for students in Grades 9-10.

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