The equation you provided, \( y = 3x + 6 \), represents a linear equation in slope-intercept form, which is \( y = mx + b \), where:

- \( m \) is the slope of the line (in this case, 3).
- \( b \) is the y-intercept, or the point where the line crosses the y-axis (in this case, 6).

### Key details:
- The slope of 3 indicates that for every 1 unit increase in \( x \), \( y \) increases by 3 units.
- The y-intercept at \( (0, 6) \) shows that when \( x = 0 \), \( y = 6 \).

This equation describes a straight line with an upward slope.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the graph of the equation \( y = 3x + 6 \)?
2. How do we find the x-intercept of the equation?
3. How does changing the slope affect the line?
4. Can we find the equation of a line parallel to this one?
5. What happens if we set \( y = 0 \)? What is \( x \)?

**Tip:** The slope of a line represents how steep the line is, and a larger slope means the line rises or falls more quickly.

Explore the linear equation y=3x+6, covering key concepts such as slope and y-intercept. Learn how to interpret the slope-intercept form and understand how changes in x affect y. Suitable for students in Grades 6-8.

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