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?

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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 \( x \)).

Learn how to graph the linear function f(x) = 3x with a step-by-step solution. Understand the slope-intercept form, plot points on the graph, and draw the line through the origin. Suitable for students in Grades 6-8, covering key algebra concepts.

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