The given function is \( P(x) = -\frac{1}{2}x + 2 \). 

This represents a linear function in the form \( P(x) = mx + b \), where:
- \( m \) is the slope of the line, which in this case is \( -\frac{1}{2} \).
- \( b \) is the y-intercept, which here is 2.

### Key Characteristics:
1. **Slope**: \( -\frac{1}{2} \) means that for every unit increase in \( x \), the value of \( P(x) \) decreases by \( \frac{1}{2} \).
2. **Y-intercept**: The line crosses the y-axis at \( P(0) = 2 \).
3. **X-intercept**: To find the x-intercept, set \( P(x) = 0 \) and solve for \( x \):
   \[
   0 = -\frac{1}{2}x + 2
   \]
   \[
   \frac{1}{2}x = 2 \implies x = 4
   \]
   So the x-intercept is at \( x = 4 \).

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What is the significance of the slope in the context of this linear function?
2. How would the graph of the function change if the slope were positive?
3. What happens to the graph if the y-intercept is changed to a different value?
4. How do you calculate the distance between the x-intercept and y-intercept?
5. What is the equation of a line parallel to \( P(x) \) that passes through a different point?

**Tip:** When dealing with linear equations, always start by identifying the slope and y-intercept, as they provide crucial information about the line's behavior.

Explore the linear function P(x) = -1/2x + 2 with detailed insights into its slope, y-intercept, and x-intercept. This problem illustrates fundamental concepts in algebra, including linear functions and their graphical representation. Suitable for Grades 7-9 students.

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