To find the value of $f(4)$, let's first analyze the graph of the function.

1. Identify the Line’s Equation: The line appears to be linear, so it follows the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Determine the Slope (m): Looking at the graph, the line appears to descend as it moves from left to right, indicating a negative slope. We can calculate the slope by taking two points on the line. For example, let’s assume two points:

   • Point 1: $(-2, 4)$
   • Point 2: $(0, 2)$

   Using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{0 - (-2)} = \frac{-2}{2} = -1$

   So, the slope $m$ is $-1$.

3. Find the y-intercept (b): The line crosses the y-axis at $y = 2$, so the y-intercept $b$ is $2$.

   Therefore, the equation of the line is: $f(x) = -x + 2$

4. Calculate $f(4)$: Substitute $x = 4$ into the equation: $f(4) = -(4) + 2 = -4 + 2 = -2$

So, $f(4) = -2$.

Would you like further details on any part of this process?

Here are some related questions you might find interesting:

1. How would you calculate the slope if the points given were different?
2. How can you determine the equation of a line if you only know the slope and one point?
3. What is the significance of the y-intercept in a linear function?
4. How do you interpret a negative slope in terms of the relationship between $x$ and $y$?
5. How would you graph a line if only the equation was given?

Tip: When reading a graph, carefully choose points where the line crosses exact coordinates to simplify calculations for slope and intercept.