The given equation is:

\[
y - 6x = 3
\]

We can solve this equation for \( y \) to express it in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Steps:
1. Add \( 6x \) to both sides of the equation:

\[
y = 6x + 3
\]

Now, the equation is in the form \( y = mx + b \), where:
- Slope \( m = 6 \)
- Y-intercept \( b = 3 \)

### Interpretation:
- The slope is 6, which means for every 1 unit increase in \( x \), \( y \) increases by 6 units.
- The y-intercept is 3, meaning the line crosses the y-axis at \( y = 3 \).

Would you like more details on how to graph this equation or how it relates to other concepts?

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Here are 5 related questions:
1. What is the equation of a line parallel to \( y = 6x + 3 \)?
2. How would the equation change if the slope were negative?
3. What is the x-intercept of the line \( y = 6x + 3 \)?
4. How would you write the equation in point-slope form?
5. What is the perpendicular slope to the line \( y = 6x + 3 \)?

**Tip:** In slope-intercept form, the coefficient of \( x \) is always the slope, and the constant term is the y-intercept.

Learn how to solve the linear equation Y - 6x = 3 and express it in slope-intercept form. This problem demonstrates key algebraic concepts, including calculating the slope and y-intercept. Suitable for students in Grades 7-10.

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