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The question asks to determine the x- and y-intercepts of the line given by the equation \( 2x + y = 4 \), and then to graph the line. Let's go through each part step-by-step.

### Step 1: Finding the Intercepts

1. **X-Intercept**: This is the point where the line crosses the x-axis, so \( y = 0 \).
   - Substitute \( y = 0 \) into the equation \( 2x + y = 4 \):
     \[
     2x + 0 = 4 \Rightarrow 2x = 4 \Rightarrow x = 2
     \]
   - Therefore, the x-intercept is \( (2, 0) \).

2. **Y-Intercept**: This is the point where the line crosses the y-axis, so \( x = 0 \).
   - Substitute \( x = 0 \) into the equation \( 2x + y = 4 \):
     \[
     2(0) + y = 4 \Rightarrow y = 4
     \]
   - Therefore, the y-intercept is \( (0, 4) \).

### Step 2: Graphing the Line

To graph the line, you would plot the two intercepts:
- Plot the x-intercept at \( (2, 0) \).
- Plot the y-intercept at \( (0, 4) \).

Draw a straight line through these two points, as this line represents all points \((x, y)\) that satisfy the equation \( 2x + y = 4 \).

Would you like me to provide a detailed graph for visualization?

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### Additional Questions

1. What is the slope of the line \( 2x + y = 4 \)?
2. How would the graph change if the equation were \( 2x + y = 6 \) instead of \( 2x + y = 4 \)?
3. Can you express \( 2x + y = 4 \) in slope-intercept form?
4. How do you find the intercepts for a line given in a different form, like \( y = 3x + 1 \)?
5. What is the significance of the x- and y-intercepts in real-world applications?

### Tip
For linear equations, remember that finding the intercepts is often a quick way to sketch the line without needing to plot many points.

Determine the x- and y-intercepts of 2x + y = 4 and graph the line.

Learn how to determine the x- and y-intercepts of the equation 2x + y = 4 and graph the line. This lesson covers key concepts in linear algebra and graphing techniques, suitable for students in Grades 8-10.

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