To create a line graph for the equation \( y = 3x - 4 \), follow these steps:

1. **Identify the slope and y-intercept**:
   - The equation is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Slope \( m = 3 \) (meaning the line rises by 3 units for every 1 unit it moves right).
   - Y-intercept \( b = -4 \) (meaning the line crosses the y-axis at \( y = -4 \)).

2. **Plot points**:
   - Start by plotting the y-intercept \( (0, -4) \).
   - Using the slope, from \( (0, -4) \), move up 3 units and 1 unit to the right to get another point \( (1, -1) \).
   - Repeat this process for more points or go backward by going down 3 units and 1 unit to the left.

3. **Draw the line**:
   - After plotting the points, draw a straight line through them.

I'll generate a graph for you:

Here is the line graph for the equation \( y = 3x - 4 \). The red point marks the y-intercept at \( (0, -4) \), and the slope determines the angle of the line.

Would you like more details on how this was generated or any specific part of the process? 

Here are some related questions for you to explore:

1. How does the slope affect the steepness of a line?
2. What happens to the graph if the slope is negative?
3. How would you graph the line if the equation were \( y = -3x + 2 \)?
4. What are the steps to convert an equation into slope-intercept form?
5. How do you find the x-intercept of a line?

**Tip**: The y-intercept \( b \) in the equation \( y = mx + b \) always tells you where the line crosses the y-axis.

Learn how to graph the linear equation y=3x-4 by identifying the slope and y-intercept. Follow the step-by-step process to plot points and draw the line, suitable for Grades 7-9 students.

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