The given function is $f(x) = 3 - 6x$, which is a linear equation in the slope-intercept form $f(x) = mx + b$, where:

• $m$ is the slope,
• $b$ is the y-intercept.

For this function:

• The slope $m = -6$,
• The y-intercept $b = 3$.

Steps to graph:

1. Plot the y-intercept: The point where the line crosses the y-axis is $(0, 3)$.
2. Use the slope: The slope $m = -6$ means for every 1 unit you move to the right (positive x-direction), you move 6 units down (negative y-direction). Starting from $(0, 3)$, move to the point $(1, -3)$.
3. Draw the line: Connect the points $(0, 3)$ and $(1, -3)$ with a straight line, and extend it in both directions.

This will give you the graph of the function.

Would you like me to draw the graph for you? If yes, I can generate an image.

Questions:

1. What is the significance of the slope in a linear equation?
2. How do we interpret the y-intercept in real-world problems?
3. How does changing the slope affect the steepness of the line?
4. What happens to the graph if the y-intercept changes?
5. Can you find the x-intercept of the given function?

Tip:

To find the x-intercept of any function, set $f(x) = 0$ and solve for $x$.