To solve this problem, let's carefully examine the given information:

The equation of the graph is given as $y = -f(x - 3)$, which indicates two transformations of the function $f(x)$:

1. Horizontal Shift: The $x - 3$ part indicates a shift to the right by 3 units.
2. Reflection: The negative sign in front of $f$ means the graph is reflected across the x-axis.

Steps to solve:

1. Determine the Slope: The graph appears to have a positive slope, and we can estimate the slope by choosing two points from the graph. From the graph:

   • The line passes through the points $(3, 0)$ and $(0, -7.5)$.
   • The slope is calculated as: $\text{slope} = \frac{0 - (-7.5)}{3 - 0} = \frac{7.5}{3} = 2.5 = \frac{5}{2}$

2. Reflect the Slope: Since the equation has $-f(x - 3)$, the function is reflected, making the slope $-\frac{5}{2}$.

3. Horizontal Shift: The function is shifted right by 3 units, which means $f(x - 3)$ must be used instead of just $f(x)$. So the equation we are looking for should "undo" this shift.

4. Choose the Correct Answer: Now, we know the general form of $f(x)$ should have a slope of $\frac{5}{2}$ since the reflection has been accounted for by the $y = -f(x - 3)$ form.

Looking at the given options, the correct equation defining $f(x)$ is: $f(x) = \frac{5}{2}x + \frac{9}{2}$

Thus, the selected answer is correct.

Do you have any questions or need further details?

Here are 5 related questions to consider:

1. What is the impact of shifting a graph horizontally?
2. How does reflection across the x-axis affect the slope of a line?
3. Can you derive the slope-intercept form of a line given two points?
4. How would a vertical shift affect the equation of the function?
5. What other transformations could affect the graph of a linear function?

Tip: When determining the equation of a transformed function, always look for key transformations like translations, reflections, and dilations.