To solve this problem, we need to determine which of the lines (m, n, p, or q) matches the function $f(x) = -0.25x + 3$.

Step 1: Analyze the function $f(x) = -0.25x + 3$

• Slope: The slope is $-0.25$, meaning the line slopes downward and for every 1 unit increase in $x$, $y$ decreases by 0.25.
• Y-intercept: The y-intercept is 3, which means the line crosses the y-axis at $(0, 3)$.

Step 2: Compare with the graph

• We look for a line that:
  1. Crosses the y-axis at $y = 3$.
  2. Has a negative slope, indicating it is slanting downwards as $x$ increases.

Observations:

• Line n: Crosses the y-axis at $y = 3$ and has a negative slope. This matches the characteristics of the function $f(x) = -0.25x + 3$.
• Other lines (m, p, q) either have different y-intercepts or slopes that do not match.

Thus, line n represents the graph of the function $f(x) = -0.25x + 3$.

Would you like further details or clarifications? Here are some related questions:

1. What is the importance of the slope in identifying the correct graph?
2. How can you quickly identify the y-intercept on a graph?
3. How do changes in the slope affect the appearance of the graph?
4. How would the graph look if the slope were positive instead of negative?
5. Can a different function be represented by one of the other lines?

Tip: Always start by identifying the y-intercept and slope when analyzing a linear function graph!