https://file.aiquickdraw.com/mathbot/file/1727844166527b4ds4y6q.jpg

The expression provided in the image is:

\[
f(x) = -3x - 2
\]

This is a linear function, meaning the graph of this function will be a straight line. Here's a breakdown:

- **Slope (m):** The coefficient of \(x\) is \(-3\), which means the line has a slope of \(-3\), indicating it falls as \(x\) increases.
- **Y-intercept (b):** The constant term is \(-2\), which means the line crosses the y-axis at \(-2\).

### Steps to graph the function:
1. **Plot the y-intercept**: Start at the point \((0, -2)\) on the graph.
2. **Use the slope**: From \((0, -2)\), apply the slope \(-3\). For every step 1 unit to the right (increasing \(x\)), move 3 units down (because the slope is negative).

Would you like further details on how to draw the graph or explore specific characteristics of the function?

Here are five related questions to extend your understanding:
1. How do we find the x-intercept of a linear function like this one?
2. What is the general form of a linear equation?
3. How does changing the slope affect the steepness of a line?
4. How can we determine if two lines are parallel or perpendicular?
5. What are the implications of a positive versus a negative slope?

**Tip:** The slope of a line tells you how steep it is—larger absolute values mean steeper lines!

Learn how to graph the linear function f(x) = -3x - 2. This tutorial breaks down the steps to graph the function, including identifying the slope and y-intercept, plotting the points, and understanding how the slope affects the line. Suitable for students in Grades 7-9.

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