We are given the following properties for the linear function $f(x)$:

• $f(0) = 6$
• The slope of $f$ is $-9$

The general form of a linear function is:

$f(x) = mx + b$

Where:

• $m$ is the slope of the function, and
• $b$ is the y-intercept, which is $f(0)$.

From the given information:

• The slope $m = -9$,
• The y-intercept $b = f(0) = 6$.

So the equation of the linear function is:

$f(x) = -9x + 6$

This is the equation of the linear function with the given properties.

Would you like further details on how this form is derived? Let me know!

Here are five questions to expand your understanding:

1. How do you calculate the slope of a linear function given two points?
2. What is the significance of the y-intercept in the equation of a line?
3. How do you graph a linear function given its equation?
4. Can you derive a linear equation if you are given two points instead of the slope and intercept?
5. How does the sign of the slope affect the direction of the line?

Tip: The slope of a line tells you how much the function value changes for every unit change in $x$. Negative slopes indicate a decreasing function.