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The linear equation given is \( y = 3x + 1 \). 

This is in the slope-intercept form \( y = mx + b \), where:
- \( m = 3 \) is the slope,
- \( b = 1 \) is the y-intercept.

### Steps to graph the line:
1. **Start with the y-intercept (0, 1)**: Plot the point at \( (0, 1) \) on the y-axis.
2. **Use the slope**: The slope is \( 3 \), meaning that for every increase of 1 unit in the x-direction, the y-coordinate increases by 3 units. So, from \( (0, 1) \), move 1 unit to the right and 3 units up to find another point \( (1, 4) \).
3. **Plot another point**: Use the slope again, or go back by moving 1 unit left and 3 units down to get another point \( (-1, -2) \).
4. **Draw the line**: Connect these points with a straight line.

This line represents the equation \( y = 3x + 1 \).

Would you like further details on graphing or on interpreting linear equations?

Here are 5 related questions:
1. What happens if you change the slope in the equation?
2. How do you find the x-intercept of a linear equation?
3. What is the relationship between the slope and the steepness of the line?
4. How do you determine the direction of a line based on the sign of the slope?
5. How can you graph linear inequalities from equations like this one?

**Tip**: The y-intercept is always where the line crosses the y-axis, and it's a quick way to start graphing any linear equation.

Learn how to graph the linear equation y = 3x + 1 by identifying the slope and y-intercept. This algebra problem is perfect for students in Grades 8-10 and helps understand the slope-intercept form and graphing techniques.

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