The problem asks for the zero of a linear function $f$ that passes through the point $(1, -9)$ and has a slope of $-3$.

To find the zero of the function (where $f(x) = 0$), we can follow these steps:

1. Write the equation of the line in slope-intercept form:

The slope-intercept form is: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. We're given the slope $m = -3$, and the point $(1, -9)$ lies on the line. We can substitute these values into the equation to find $b$.

$-9 = -3(1) + b$ $-9 = -3 + b$ $b = -6$

Thus, the equation of the line is: $y = -3x - 6$

2. Find the zero of the function:

To find the zero of $f$, we need to solve for $x$ when $y = 0$: $0 = -3x - 6$ $3x = -6$ $x = -2$

Thus, the zero of the function is $x = -2$.

Answer:

The correct answer is $\boxed{-2}$, which corresponds to option C.

Let me know if you would like more details or have further questions!

Here are five follow-up questions for further exploration:

1. What is the y-intercept of the line given the equation $y = -3x - 6$?
2. How do we find the slope from two points on a line?
3. How would the graph of the equation $y = -3x - 6$ look?
4. What would the zero be if the slope was $2$ instead of $-3$?
5. How would the zero change if the y-intercept $b$ was $0$?

Tip: The zero of a function is where the graph of the function crosses the x-axis.