The equation \( y = -\frac{1}{2}x + 4 \) represents a straight line in slope-intercept form, which is \( y = mx + b \), where:

- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

For this specific equation:
- The slope \( m = -\frac{1}{2} \), indicating that for every unit increase in \( x \), \( y \) decreases by \( \frac{1}{2} \) units.
- The y-intercept \( b = 4 \), meaning the line crosses the y-axis at \( y = 4 \).

### Properties of the Line:
- **Slope:** \( -\frac{1}{2} \)
- **Y-intercept:** \( (0, 4) \)
- **X-intercept:** Set \( y = 0 \) and solve for \( x \).

To find the x-intercept:
\[
0 = -\frac{1}{2}x + 4
\]
\[
\frac{1}{2}x = 4
\]
\[
x = 8
\]
So, the x-intercept is at \( (8, 0) \).

Would you like to see the graph of this line or have any further details? 

Here are 5 questions related to this concept:
1. How do you find the slope between two points on a line?
2. What is the significance of the y-intercept in a real-world scenario?
3. How would the line change if the slope were positive?
4. Can you write the equation of a line parallel to this one?
5. How do you determine if two lines are perpendicular?

**Tip:** The sign of the slope indicates the direction of the line; a negative slope means the line descends as it moves from left to right.

Learn how to analyze the linear equation y = -1/2x + 4, covering key concepts like the slope, y-intercept, and x-intercept. This problem explains how to find the intercepts and understand the line's behavior, making it perfect for students in Grades 8-10.

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