To graph the linear function $f(x) = 3x$, follow these steps:

Step-by-Step Graphing:

1. Identify the slope and y-intercept:

   • The function is in the form $f(x) = mx + b$, where:
     • $m$ is the slope (the rate of change of $y$ with respect to $x$).
     • $b$ is the y-intercept (the point where the graph crosses the y-axis).
   • For $f(x) = 3x$, the slope $m = 3$ and the y-intercept $b = 0$.

2. Plot the y-intercept:

   • Since $b = 0$, the graph passes through the origin $(0, 0)$.

3. Use the slope to find another point:

   • The slope of 3 means that for every 1 unit increase in $x$, $y$ increases by 3.
   • Starting from $(0, 0)$, move 1 unit right (to $x = 1$) and 3 units up (to $y = 3$).
   • This gives the point $(1, 3)$.

4. Plot the second point $(1, 3)$:

   • Mark this point on the graph.

5. Draw the line:

   • Draw a straight line through the points $(0, 0)$ and $(1, 3)$.
   • Extend the line in both directions.

Summary:

• The line has a slope of 3, and it passes through the origin.
• Any point on the line follows the relationship $y = 3x$.

Would you like me to generate a graph for this?

---

Here are five related questions:

1. How does the slope of a line affect its steepness on a graph?
2. What happens to the graph if the slope of $f(x)$ changes from 3 to -3?
3. How do you find the x-intercept of a linear function?
4. Can a linear function have more than one y-intercept?
5. How would you graph the function $f(x) = 3x + 2$?

Tip: The slope of a line can be interpreted as the rise (change in $y$) over the run (change in $x$).