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To write the equation of a line with a given slope and y-intercept, we can use the **slope-intercept form** of a line equation, which is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope.
- \(b\) is the y-intercept.

In this problem:
- The slope \(m = 3\).
- The y-intercept is \((0, 6)\), meaning \(b = 6\).

So, substituting the values into the slope-intercept form, we get:

\[
y = 3x + 6
\]

This is the equation of the line with slope 3 and y-intercept at \((0, 6)\).

Would you like a deeper explanation or have any questions? 

Here are 5 related questions to expand your understanding:
1. How would the equation change if the slope were negative, say \(-3\)?
2. What is the equation of a line that passes through the point \((2, 8)\) and has a slope of \(4\)?
3. How do you find the x-intercept of the equation \(y = 3x + 6\)?
4. What is the general form of a line equation, and how can you convert the slope-intercept form to it?
5. Can you graph the line represented by \(y = 3x + 6\) and explain its key features?

**Tip**: Remember that the slope \(m\) represents how steep a line is, and the y-intercept \(b\) tells you where the line crosses the y-axis.

Write the equation of a line with slope 3 and y-intercept of (0, 6). Use x as the input variable, and y as the output variable.

Learn how to write the equation of a line with slope 3 and a y-intercept of (0, 6). This problem focuses on linear equations in slope-intercept form and is suitable for students in Grades 6-8.

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