The function you provided is \( f(x) = -2x + 12 \), which is a linear equation. Here's an analysis of it:

1. **Slope-Intercept Form**: This equation is already in the slope-intercept form \( f(x) = mx + b \), where:
   - \( m \) (slope) = -2
   - \( b \) (y-intercept) = 12

2. **Graph of the Function**:
   - The graph will be a straight line.
   - The slope \( -2 \) means the line decreases by 2 units on the y-axis for every 1 unit increase on the x-axis.
   - The y-intercept of 12 means the line crosses the y-axis at the point \( (0, 12) \).

3. **Key Points**:
   - At \( x = 0 \), \( f(0) = 12 \).
   - To find the x-intercept (where \( f(x) = 0 \)), solve \( -2x + 12 = 0 \):
     \[
     -2x = -12 \implies x = 6
     \]
     So the line crosses the x-axis at \( (6, 0) \).

4. **Domain and Range**:
   - Domain: All real numbers, \( (-\infty, \infty) \), since it's a linear function.
   - Range: All real numbers, \( (-\infty, \infty) \), because the line extends infinitely in both directions.

Do you want more details on graphing or solving?  
Here are some related questions:

1. How do you calculate the slope of a line given two points?
2. What is the significance of the slope in a linear function?
3. Can we rewrite the equation to find the x-intercept and y-intercept more easily?
4. How would we apply transformations to shift or stretch the graph of this function?
5. What are the general properties of linear functions?

**Tip**: The slope determines whether a line rises or falls—positive slopes rise, while negative slopes fall!

Discover how to solve and graph the linear equation f(x) = -2x + 12. This detailed solution explains the slope-intercept form, finding intercepts, and key points for graphing the function. Perfect for students in Grades 7-10 learning about linear equations.

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