The equation $y = -4x - 9$ is indeed a function. Here's why:

In mathematics, a relation is a function if, for every input value of $x$, there is exactly one output value of $y$. The given equation is a linear equation in slope-intercept form $y = mx + b$, where $m = -4$ and $b = -9$.

For every value of $x$, this equation produces exactly one corresponding $y$ value. Therefore, the relation satisfies the definition of a function.

Answer: Yes

Would you like additional explanations or have further questions? Here are some related concepts to explore:

1. What are the characteristics of a linear function?
2. How can you determine if a relation is a function from a graph?
3. What does the slope ($m$) represent in the equation $y = mx + b$?
4. How do you test if a relation is a function using the vertical line test?
5. What are some examples of relations that are not functions?

Tip: A quick way to confirm if an equation is a function is to check if it passes the vertical line test when graphed. If every vertical line intersects the graph at most once, it's a function!