To convert the equation $x - 6y = 2$ into slope-intercept form, we need to solve for $y$.

Steps:

1. Start with the equation: $x - 6y = 2$

2. Subtract $x$ from both sides to isolate the $y$-term: $-6y = -x + 2$

3. Divide both sides by -6 to solve for $y$: $y = \frac{-x + 2}{-6}$

4. Simplify the expression: $y = \frac{1}{6}x - \frac{1}{3}$

Final Answer:

The equation in slope-intercept form is: $y = \frac{1}{6}x - \frac{1}{3}$

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Would you like more details on this, or do you have any other questions?

Here are some related questions you might find interesting:

1. How would you convert an equation like $2x + 3y = 12$ into slope-intercept form?
2. How do you identify the slope and y-intercept from an equation in slope-intercept form?
3. How can you graph an equation once it's in slope-intercept form?
4. What is the meaning of the slope and y-intercept in a real-world context?
5. How can you write an equation in standard form from slope-intercept form?

Tip: When working with slope-intercept form, remember that the slope is the coefficient of $x$, and the y-intercept is the constant term.